id sid tid token lemma pos work_53xuaunsqfhv7cuuzotagythj4 1 1 Mathematics Mathematics NNP work_53xuaunsqfhv7cuuzotagythj4 1 2 Interdisciplinary Interdisciplinary NNP work_53xuaunsqfhv7cuuzotagythj4 1 3 Research Research NNP work_53xuaunsqfhv7cuuzotagythj4 1 4 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 1 5 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 1 6 2019 2019 CD work_53xuaunsqfhv7cuuzotagythj4 1 7 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 1 8 xx xx NNP work_53xuaunsqfhv7cuuzotagythj4 1 9 − − NNP work_53xuaunsqfhv7cuuzotagythj4 1 10 yy yy PRP$ work_53xuaunsqfhv7cuuzotagythj4 1 11 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 1 12 Ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 1 13 : : : work_53xuaunsqfhv7cuuzotagythj4 1 14 The the DT work_53xuaunsqfhv7cuuzotagythj4 1 15 Mathematics Mathematics NNPS work_53xuaunsqfhv7cuuzotagythj4 1 16 of of IN work_53xuaunsqfhv7cuuzotagythj4 1 17 Beauty Beauty NNP work_53xuaunsqfhv7cuuzotagythj4 1 18 Hamid Hamid NNP work_53xuaunsqfhv7cuuzotagythj4 1 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work_53xuaunsqfhv7cuuzotagythj4 5 23 rhythmic rhythmic JJ work_53xuaunsqfhv7cuuzotagythj4 5 24 balance balance NN work_53xuaunsqfhv7cuuzotagythj4 5 25 which which WDT work_53xuaunsqfhv7cuuzotagythj4 5 26 according accord VBG work_53xuaunsqfhv7cuuzotagythj4 5 27 to to IN work_53xuaunsqfhv7cuuzotagythj4 5 28 most most JJS work_53xuaunsqfhv7cuuzotagythj4 5 29 experts expert NNS work_53xuaunsqfhv7cuuzotagythj4 5 30 the the DT work_53xuaunsqfhv7cuuzotagythj4 5 31 reason reason NN work_53xuaunsqfhv7cuuzotagythj4 5 32 lies lie VBZ work_53xuaunsqfhv7cuuzotagythj4 5 33 in in IN work_53xuaunsqfhv7cuuzotagythj4 5 34 using use VBG work_53xuaunsqfhv7cuuzotagythj4 5 35 the the DT work_53xuaunsqfhv7cuuzotagythj4 5 36 ratios ratio NNS work_53xuaunsqfhv7cuuzotagythj4 5 37 . . . work_53xuaunsqfhv7cuuzotagythj4 6 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 6 2 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 6 3 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 6 4 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 6 5 been be VBN work_53xuaunsqfhv7cuuzotagythj4 6 6 used use VBN work_53xuaunsqfhv7cuuzotagythj4 6 7 to to TO work_53xuaunsqfhv7cuuzotagythj4 6 8 analyze analyze VB work_53xuaunsqfhv7cuuzotagythj4 6 9 the the DT work_53xuaunsqfhv7cuuzotagythj4 6 10 proportions proportion NNS work_53xuaunsqfhv7cuuzotagythj4 6 11 of of IN work_53xuaunsqfhv7cuuzotagythj4 6 12 natural natural JJ work_53xuaunsqfhv7cuuzotagythj4 6 13 objects object NNS work_53xuaunsqfhv7cuuzotagythj4 6 14 as as RB work_53xuaunsqfhv7cuuzotagythj4 6 15 well well RB work_53xuaunsqfhv7cuuzotagythj4 6 16 as as IN work_53xuaunsqfhv7cuuzotagythj4 6 17 buildings building NNS work_53xuaunsqfhv7cuuzotagythj4 6 18 harmony harmony NN work_53xuaunsqfhv7cuuzotagythj4 6 19 . . . work_53xuaunsqfhv7cuuzotagythj4 7 1 In in IN work_53xuaunsqfhv7cuuzotagythj4 7 2 this this DT work_53xuaunsqfhv7cuuzotagythj4 7 3 paper paper NN work_53xuaunsqfhv7cuuzotagythj4 7 4 , , , work_53xuaunsqfhv7cuuzotagythj4 7 5 after 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work_53xuaunsqfhv7cuuzotagythj4 7 25 nature nature NN work_53xuaunsqfhv7cuuzotagythj4 7 26 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 7 27 discussed discuss VBN work_53xuaunsqfhv7cuuzotagythj4 7 28 . . . work_53xuaunsqfhv7cuuzotagythj4 8 1 When when WRB work_53xuaunsqfhv7cuuzotagythj4 8 2 teaching teach VBG work_53xuaunsqfhv7cuuzotagythj4 8 3 mathematics mathematic NNS work_53xuaunsqfhv7cuuzotagythj4 8 4 in in IN work_53xuaunsqfhv7cuuzotagythj4 8 5 the the DT work_53xuaunsqfhv7cuuzotagythj4 8 6 schools school NNS work_53xuaunsqfhv7cuuzotagythj4 8 7 , , , work_53xuaunsqfhv7cuuzotagythj4 8 8 one one PRP work_53xuaunsqfhv7cuuzotagythj4 8 9 may may MD work_53xuaunsqfhv7cuuzotagythj4 8 10 refer refer VB work_53xuaunsqfhv7cuuzotagythj4 8 11 to to IN work_53xuaunsqfhv7cuuzotagythj4 8 12 this this DT work_53xuaunsqfhv7cuuzotagythj4 8 13 interconnection interconnection NN work_53xuaunsqfhv7cuuzotagythj4 8 14 to to TO work_53xuaunsqfhv7cuuzotagythj4 8 15 encourage encourage VB work_53xuaunsqfhv7cuuzotagythj4 8 16 students student NNS work_53xuaunsqfhv7cuuzotagythj4 8 17 to to TO work_53xuaunsqfhv7cuuzotagythj4 8 18 feel feel VB work_53xuaunsqfhv7cuuzotagythj4 8 19 better well JJR work_53xuaunsqfhv7cuuzotagythj4 8 20 with with IN work_53xuaunsqfhv7cuuzotagythj4 8 21 mathematics mathematic NNS work_53xuaunsqfhv7cuuzotagythj4 8 22 and and CC work_53xuaunsqfhv7cuuzotagythj4 8 23 deepen deepen VB work_53xuaunsqfhv7cuuzotagythj4 8 24 their -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 8 25 understanding understanding NN work_53xuaunsqfhv7cuuzotagythj4 8 26 of of IN work_53xuaunsqfhv7cuuzotagythj4 8 27 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 8 28 . . . work_53xuaunsqfhv7cuuzotagythj4 9 1 At at IN work_53xuaunsqfhv7cuuzotagythj4 9 2 the the DT work_53xuaunsqfhv7cuuzotagythj4 9 3 end end NN work_53xuaunsqfhv7cuuzotagythj4 9 4 , , , work_53xuaunsqfhv7cuuzotagythj4 9 5 the the DT work_53xuaunsqfhv7cuuzotagythj4 9 6 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 9 7 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 9 8 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 9 9 been be VBN work_53xuaunsqfhv7cuuzotagythj4 9 10 statistically statistically RB work_53xuaunsqfhv7cuuzotagythj4 9 11 examined examine VBN work_53xuaunsqfhv7cuuzotagythj4 9 12 using use VBG work_53xuaunsqfhv7cuuzotagythj4 9 13 its -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 9 14 first first JJ work_53xuaunsqfhv7cuuzotagythj4 9 15 100000 100000 CD work_53xuaunsqfhv7cuuzotagythj4 9 16 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 9 17 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 9 18 to to TO work_53xuaunsqfhv7cuuzotagythj4 9 19 show show VB work_53xuaunsqfhv7cuuzotagythj4 9 20 that that IN work_53xuaunsqfhv7cuuzotagythj4 9 21 the the DT work_53xuaunsqfhv7cuuzotagythj4 9 22 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 9 23 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 9 24 decimals decimal NNS work_53xuaunsqfhv7cuuzotagythj4 9 25 can can MD work_53xuaunsqfhv7cuuzotagythj4 9 26 be be VB work_53xuaunsqfhv7cuuzotagythj4 9 27 used use VBN work_53xuaunsqfhv7cuuzotagythj4 9 28 as as IN work_53xuaunsqfhv7cuuzotagythj4 9 29 a a DT work_53xuaunsqfhv7cuuzotagythj4 9 30 random random JJ work_53xuaunsqfhv7cuuzotagythj4 9 31 number number NN work_53xuaunsqfhv7cuuzotagythj4 9 32 generator generator NN work_53xuaunsqfhv7cuuzotagythj4 9 33 . . . work_53xuaunsqfhv7cuuzotagythj4 10 1 Keywords keyword NNS work_53xuaunsqfhv7cuuzotagythj4 10 2 : : : work_53xuaunsqfhv7cuuzotagythj4 10 3 Fibonacci fibonacci NN work_53xuaunsqfhv7cuuzotagythj4 10 4 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 10 5 , , , work_53xuaunsqfhv7cuuzotagythj4 10 6 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 10 7 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 10 8 , , , work_53xuaunsqfhv7cuuzotagythj4 10 9 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 10 10 rectangular rectangular NN work_53xuaunsqfhv7cuuzotagythj4 10 11 , , , work_53xuaunsqfhv7cuuzotagythj4 10 12 random random JJ work_53xuaunsqfhv7cuuzotagythj4 10 13 number number NN work_53xuaunsqfhv7cuuzotagythj4 10 14 generator generator NN work_53xuaunsqfhv7cuuzotagythj4 10 15 . . . work_53xuaunsqfhv7cuuzotagythj4 11 1 2010 2010 CD work_53xuaunsqfhv7cuuzotagythj4 11 2 Mathematics Mathematics NNP work_53xuaunsqfhv7cuuzotagythj4 11 3 Subject Subject NNP work_53xuaunsqfhv7cuuzotagythj4 11 4 Classification classification NN work_53xuaunsqfhv7cuuzotagythj4 11 5 : : : work_53xuaunsqfhv7cuuzotagythj4 11 6 Primary primary JJ work_53xuaunsqfhv7cuuzotagythj4 11 7 00A67 00a67 CD work_53xuaunsqfhv7cuuzotagythj4 11 8 , , , work_53xuaunsqfhv7cuuzotagythj4 11 9 00A66 00a66 CD work_53xuaunsqfhv7cuuzotagythj4 11 10 , , , work_53xuaunsqfhv7cuuzotagythj4 11 11 Secondary secondary JJ work_53xuaunsqfhv7cuuzotagythj4 11 12 97A30 97a30 CD work_53xuaunsqfhv7cuuzotagythj4 11 13 . . . work_53xuaunsqfhv7cuuzotagythj4 12 1 How how WRB work_53xuaunsqfhv7cuuzotagythj4 12 2 to to TO 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NNP work_53xuaunsqfhv7cuuzotagythj4 12 7 Ghorbani Ghorbani NNP work_53xuaunsqfhv7cuuzotagythj4 12 8 , , , work_53xuaunsqfhv7cuuzotagythj4 12 9 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 12 10 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 12 11 : : : work_53xuaunsqfhv7cuuzotagythj4 12 12 The the DT work_53xuaunsqfhv7cuuzotagythj4 12 13 mathematics mathematic NNS work_53xuaunsqfhv7cuuzotagythj4 12 14 of of IN work_53xuaunsqfhv7cuuzotagythj4 12 15 beauty beauty NN work_53xuaunsqfhv7cuuzotagythj4 12 16 , , , work_53xuaunsqfhv7cuuzotagythj4 12 17 Math math NN work_53xuaunsqfhv7cuuzotagythj4 12 18 . . . work_53xuaunsqfhv7cuuzotagythj4 13 1 Interdisc Interdisc NNP work_53xuaunsqfhv7cuuzotagythj4 13 2 . . . work_53xuaunsqfhv7cuuzotagythj4 14 1 Res Res NNP work_53xuaunsqfhv7cuuzotagythj4 14 2 . . . work_53xuaunsqfhv7cuuzotagythj4 15 1 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 15 2 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 15 3 2019 2019 CD work_53xuaunsqfhv7cuuzotagythj4 15 4 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 15 5 xx xx CD work_53xuaunsqfhv7cuuzotagythj4 15 6 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 15 7 yy yy NN work_53xuaunsqfhv7cuuzotagythj4 15 8 . . . work_53xuaunsqfhv7cuuzotagythj4 16 1 1 1 LS work_53xuaunsqfhv7cuuzotagythj4 16 2 . . . work_53xuaunsqfhv7cuuzotagythj4 17 1 Introduction Introduction NNP work_53xuaunsqfhv7cuuzotagythj4 17 2 Proportions Proportions NNP work_53xuaunsqfhv7cuuzotagythj4 17 3 in in IN work_53xuaunsqfhv7cuuzotagythj4 17 4 geometry geometry NN work_53xuaunsqfhv7cuuzotagythj4 17 5 , , , work_53xuaunsqfhv7cuuzotagythj4 17 6 architecture architecture NN work_53xuaunsqfhv7cuuzotagythj4 17 7 , , , work_53xuaunsqfhv7cuuzotagythj4 17 8 music music NN work_53xuaunsqfhv7cuuzotagythj4 17 9 and and CC work_53xuaunsqfhv7cuuzotagythj4 17 10 art art NN work_53xuaunsqfhv7cuuzotagythj4 17 11 express express VBP work_53xuaunsqfhv7cuuzotagythj4 17 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 17 13 harmonious harmonious JJ 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work_53xuaunsqfhv7cuuzotagythj4 29 48 line line NN work_53xuaunsqfhv7cuuzotagythj4 29 49 segment segment NN work_53xuaunsqfhv7cuuzotagythj4 29 50 with with IN work_53xuaunsqfhv7cuuzotagythj4 29 51 endpoints endpoint NNS work_53xuaunsqfhv7cuuzotagythj4 29 52 A A NNP work_53xuaunsqfhv7cuuzotagythj4 29 53 and and CC work_53xuaunsqfhv7cuuzotagythj4 29 54 B b NN work_53xuaunsqfhv7cuuzotagythj4 29 55 and and CC work_53xuaunsqfhv7cuuzotagythj4 29 56 its -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 29 57 length length NN work_53xuaunsqfhv7cuuzotagythj4 29 58 , , , work_53xuaunsqfhv7cuuzotagythj4 29 59 respectively respectively RB work_53xuaunsqfhv7cuuzotagythj4 29 60 . . . work_53xuaunsqfhv7cuuzotagythj4 30 1 In in IN work_53xuaunsqfhv7cuuzotagythj4 30 2 the the DT work_53xuaunsqfhv7cuuzotagythj4 30 3 Book Book NNP work_53xuaunsqfhv7cuuzotagythj4 30 4 VI VI NNP work_53xuaunsqfhv7cuuzotagythj4 30 5 , , , work_53xuaunsqfhv7cuuzotagythj4 30 6 he -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 30 7 defines define VBZ work_53xuaunsqfhv7cuuzotagythj4 30 8 that that IN work_53xuaunsqfhv7cuuzotagythj4 30 9 the the DT work_53xuaunsqfhv7cuuzotagythj4 30 10 segment segment NN work_53xuaunsqfhv7cuuzotagythj4 30 11 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 30 12 AB AB NNP work_53xuaunsqfhv7cuuzotagythj4 30 13 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 30 14 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 30 15 divided divide VBN work_53xuaunsqfhv7cuuzotagythj4 30 16 in in IN work_53xuaunsqfhv7cuuzotagythj4 30 17 extreme extreme JJ work_53xuaunsqfhv7cuuzotagythj4 30 18 and and CC work_53xuaunsqfhv7cuuzotagythj4 30 19 mean mean VB work_53xuaunsqfhv7cuuzotagythj4 30 20 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 30 21 by by IN work_53xuaunsqfhv7cuuzotagythj4 30 22 a a DT work_53xuaunsqfhv7cuuzotagythj4 30 23 point point NN work_53xuaunsqfhv7cuuzotagythj4 30 24 C c NN work_53xuaunsqfhv7cuuzotagythj4 30 25 ∈ ∈ VBG work_53xuaunsqfhv7cuuzotagythj4 30 26 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 30 27 AB AB NNP work_53xuaunsqfhv7cuuzotagythj4 30 28 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 30 29 , , , work_53xuaunsqfhv7cuuzotagythj4 30 30 if if IN work_53xuaunsqfhv7cuuzotagythj4 30 31 AC AC NNP work_53xuaunsqfhv7cuuzotagythj4 30 32 < < XX work_53xuaunsqfhv7cuuzotagythj4 30 33 CB CB NNP work_53xuaunsqfhv7cuuzotagythj4 30 34 and and CC work_53xuaunsqfhv7cuuzotagythj4 30 35 CB CB NNP work_53xuaunsqfhv7cuuzotagythj4 30 36 AC AC NNP work_53xuaunsqfhv7cuuzotagythj4 30 37 = = SYM work_53xuaunsqfhv7cuuzotagythj4 30 38 AB AB NNP work_53xuaunsqfhv7cuuzotagythj4 30 39 CB CB NNP work_53xuaunsqfhv7cuuzotagythj4 30 40 . . . work_53xuaunsqfhv7cuuzotagythj4 31 1 While while IN work_53xuaunsqfhv7cuuzotagythj4 31 2 the the DT work_53xuaunsqfhv7cuuzotagythj4 31 3 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 31 4 CB CB NNP work_53xuaunsqfhv7cuuzotagythj4 31 5 AC AC NNP work_53xuaunsqfhv7cuuzotagythj4 31 6 known know VBN work_53xuaunsqfhv7cuuzotagythj4 31 7 as as IN 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CC work_53xuaunsqfhv7cuuzotagythj4 31 27 applied apply VBN work_53xuaunsqfhv7cuuzotagythj4 31 28 by by IN work_53xuaunsqfhv7cuuzotagythj4 31 29 mankind mankind NN work_53xuaunsqfhv7cuuzotagythj4 31 30 . . . work_53xuaunsqfhv7cuuzotagythj4 32 1 It -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 32 2 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 32 3 reasonable reasonable JJ work_53xuaunsqfhv7cuuzotagythj4 32 4 to to TO work_53xuaunsqfhv7cuuzotagythj4 32 5 assume assume VB work_53xuaunsqfhv7cuuzotagythj4 32 6 that that IN work_53xuaunsqfhv7cuuzotagythj4 32 7 it -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 32 8 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 32 9 perhaps perhaps RB work_53xuaunsqfhv7cuuzotagythj4 32 10 been be VBN work_53xuaunsqfhv7cuuzotagythj4 32 11 discovered discover VBN work_53xuaunsqfhv7cuuzotagythj4 32 12 and and CC work_53xuaunsqfhv7cuuzotagythj4 32 13 rediscovered rediscover VBN work_53xuaunsqfhv7cuuzotagythj4 32 14 throughout throughout IN work_53xuaunsqfhv7cuuzotagythj4 32 15 history history NN work_53xuaunsqfhv7cuuzotagythj4 32 16 , , , work_53xuaunsqfhv7cuuzotagythj4 32 17 which which WDT work_53xuaunsqfhv7cuuzotagythj4 32 18 explains explain VBZ work_53xuaunsqfhv7cuuzotagythj4 32 19 why why WRB work_53xuaunsqfhv7cuuzotagythj4 32 20 it -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 32 21 goes go VBZ work_53xuaunsqfhv7cuuzotagythj4 32 22 under under IN work_53xuaunsqfhv7cuuzotagythj4 32 23 several several JJ work_53xuaunsqfhv7cuuzotagythj4 32 24 names name NNS work_53xuaunsqfhv7cuuzotagythj4 32 25 , , , work_53xuaunsqfhv7cuuzotagythj4 32 26 such such JJ work_53xuaunsqfhv7cuuzotagythj4 32 27 as as IN work_53xuaunsqfhv7cuuzotagythj4 32 28 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 32 29 section section NN work_53xuaunsqfhv7cuuzotagythj4 32 30 , , , work_53xuaunsqfhv7cuuzotagythj4 32 31 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 32 32 mean mean NN work_53xuaunsqfhv7cuuzotagythj4 32 33 , , , work_53xuaunsqfhv7cuuzotagythj4 32 34 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 32 35 number number NN work_53xuaunsqfhv7cuuzotagythj4 32 36 , , , work_53xuaunsqfhv7cuuzotagythj4 32 37 divine divine JJ work_53xuaunsqfhv7cuuzotagythj4 32 38 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 32 39 , , , work_53xuaunsqfhv7cuuzotagythj4 32 40 divine divine JJ work_53xuaunsqfhv7cuuzotagythj4 32 41 section section NN work_53xuaunsqfhv7cuuzotagythj4 32 42 and and CC work_53xuaunsqfhv7cuuzotagythj4 32 43 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 32 44 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 32 45 . . . work_53xuaunsqfhv7cuuzotagythj4 33 1 Its -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 33 2 beautiful beautiful JJ work_53xuaunsqfhv7cuuzotagythj4 33 3 properties property NNS work_53xuaunsqfhv7cuuzotagythj4 33 4 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 33 5 won win VBN work_53xuaunsqfhv7cuuzotagythj4 33 6 the the DT work_53xuaunsqfhv7cuuzotagythj4 33 7 interest interest NN work_53xuaunsqfhv7cuuzotagythj4 33 8 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history history NN work_53xuaunsqfhv7cuuzotagythj4 34 6 , , , work_53xuaunsqfhv7cuuzotagythj4 34 7 such such JJ work_53xuaunsqfhv7cuuzotagythj4 34 8 as as IN work_53xuaunsqfhv7cuuzotagythj4 34 9 , , , work_53xuaunsqfhv7cuuzotagythj4 34 10 Le Le NNP work_53xuaunsqfhv7cuuzotagythj4 34 11 Corbusier Corbusier NNP work_53xuaunsqfhv7cuuzotagythj4 34 12 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 34 13 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 34 14 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 34 15 , , , work_53xuaunsqfhv7cuuzotagythj4 34 16 Pacioli Pacioli NNP work_53xuaunsqfhv7cuuzotagythj4 34 17 , , , work_53xuaunsqfhv7cuuzotagythj4 34 18 and and CC work_53xuaunsqfhv7cuuzotagythj4 34 19 Leonardo Leonardo NNP work_53xuaunsqfhv7cuuzotagythj4 34 20 Da Da NNP work_53xuaunsqfhv7cuuzotagythj4 34 21 Vinci Vinci NNP work_53xuaunsqfhv7cuuzotagythj4 34 22 have have VBP work_53xuaunsqfhv7cuuzotagythj4 34 23 used use VBN work_53xuaunsqfhv7cuuzotagythj4 34 24 the the DT work_53xuaunsqfhv7cuuzotagythj4 34 25 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work_53xuaunsqfhv7cuuzotagythj4 35 13 basis basis NN work_53xuaunsqfhv7cuuzotagythj4 35 14 to to IN work_53xuaunsqfhv7cuuzotagythj4 35 15 painting painting NN work_53xuaunsqfhv7cuuzotagythj4 35 16 , , , work_53xuaunsqfhv7cuuzotagythj4 35 17 published publish VBD work_53xuaunsqfhv7cuuzotagythj4 35 18 the the DT work_53xuaunsqfhv7cuuzotagythj4 35 19 book book NN work_53xuaunsqfhv7cuuzotagythj4 35 20 De De NNP work_53xuaunsqfhv7cuuzotagythj4 35 21 Divina Divina NNP work_53xuaunsqfhv7cuuzotagythj4 35 22 Proporzione Proporzione NNP work_53xuaunsqfhv7cuuzotagythj4 35 23 and and CC work_53xuaunsqfhv7cuuzotagythj4 35 24 Leonardo Leonardo NNP work_53xuaunsqfhv7cuuzotagythj4 35 25 da da NNP work_53xuaunsqfhv7cuuzotagythj4 35 26 Vinci Vinci NNP work_53xuaunsqfhv7cuuzotagythj4 35 27 made make VBD work_53xuaunsqfhv7cuuzotagythj4 35 28 the the DT work_53xuaunsqfhv7cuuzotagythj4 35 29 illustrations illustration NNS work_53xuaunsqfhv7cuuzotagythj4 35 30 of of IN work_53xuaunsqfhv7cuuzotagythj4 35 31 his -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 35 32 book book NN work_53xuaunsqfhv7cuuzotagythj4 35 33 . . . work_53xuaunsqfhv7cuuzotagythj4 36 1 In in IN work_53xuaunsqfhv7cuuzotagythj4 36 2 addition addition NN work_53xuaunsqfhv7cuuzotagythj4 36 3 , , , work_53xuaunsqfhv7cuuzotagythj4 36 4 many many JJ work_53xuaunsqfhv7cuuzotagythj4 36 5 recent recent JJ work_53xuaunsqfhv7cuuzotagythj4 36 6 publications publication NNS work_53xuaunsqfhv7cuuzotagythj4 36 7 discussed discuss VBD work_53xuaunsqfhv7cuuzotagythj4 36 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 36 9 appearance appearance NN work_53xuaunsqfhv7cuuzotagythj4 36 10 of of IN work_53xuaunsqfhv7cuuzotagythj4 36 11 the the DT work_53xuaunsqfhv7cuuzotagythj4 36 12 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 36 13 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 36 14 in in IN work_53xuaunsqfhv7cuuzotagythj4 36 15 designing design VBG work_53xuaunsqfhv7cuuzotagythj4 36 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 36 17 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Mathematics NNP work_53xuaunsqfhv7cuuzotagythj4 38 6 In in IN work_53xuaunsqfhv7cuuzotagythj4 38 7 mathematics mathematic NNS work_53xuaunsqfhv7cuuzotagythj4 38 8 two two CD work_53xuaunsqfhv7cuuzotagythj4 38 9 quantities quantity NNS work_53xuaunsqfhv7cuuzotagythj4 38 10 are be VBP work_53xuaunsqfhv7cuuzotagythj4 38 11 in in IN work_53xuaunsqfhv7cuuzotagythj4 38 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 38 13 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 38 14 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 38 15 if if IN work_53xuaunsqfhv7cuuzotagythj4 38 16 their -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 38 17 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 38 18 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 38 19 the the DT work_53xuaunsqfhv7cuuzotagythj4 38 20 same same JJ work_53xuaunsqfhv7cuuzotagythj4 38 21 as as IN work_53xuaunsqfhv7cuuzotagythj4 38 22 the the DT work_53xuaunsqfhv7cuuzotagythj4 38 23 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 38 24 of of IN work_53xuaunsqfhv7cuuzotagythj4 38 25 their -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 38 26 sum sum NN work_53xuaunsqfhv7cuuzotagythj4 38 27 to to IN work_53xuaunsqfhv7cuuzotagythj4 38 28 the the DT work_53xuaunsqfhv7cuuzotagythj4 38 29 larger large JJR work_53xuaunsqfhv7cuuzotagythj4 38 30 of of IN work_53xuaunsqfhv7cuuzotagythj4 38 31 the the DT work_53xuaunsqfhv7cuuzotagythj4 38 32 two two CD work_53xuaunsqfhv7cuuzotagythj4 38 33 quantities quantity NNS work_53xuaunsqfhv7cuuzotagythj4 38 34 . . . work_53xuaunsqfhv7cuuzotagythj4 39 1 Expressed express VBN work_53xuaunsqfhv7cuuzotagythj4 39 2 algebraically algebraically RB work_53xuaunsqfhv7cuuzotagythj4 39 3 , , , work_53xuaunsqfhv7cuuzotagythj4 39 4 for for IN work_53xuaunsqfhv7cuuzotagythj4 39 5 quantities quantity NNS work_53xuaunsqfhv7cuuzotagythj4 39 6 a a NN work_53xuaunsqfhv7cuuzotagythj4 39 7 and and CC work_53xuaunsqfhv7cuuzotagythj4 39 8 b b NN work_53xuaunsqfhv7cuuzotagythj4 39 9 with with IN work_53xuaunsqfhv7cuuzotagythj4 39 10 a a DT work_53xuaunsqfhv7cuuzotagythj4 39 11 > > XX work_53xuaunsqfhv7cuuzotagythj4 39 12 b b NN work_53xuaunsqfhv7cuuzotagythj4 39 13 > > NNP work_53xuaunsqfhv7cuuzotagythj4 39 14 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 39 15 , , , work_53xuaunsqfhv7cuuzotagythj4 39 16 a a NN work_53xuaunsqfhv7cuuzotagythj4 39 17 + + SYM work_53xuaunsqfhv7cuuzotagythj4 39 18 b b NN work_53xuaunsqfhv7cuuzotagythj4 39 19 a a NN work_53xuaunsqfhv7cuuzotagythj4 39 20 = = SYM work_53xuaunsqfhv7cuuzotagythj4 39 21 a a DT work_53xuaunsqfhv7cuuzotagythj4 39 22 b b NN work_53xuaunsqfhv7cuuzotagythj4 39 23 def def NN work_53xuaunsqfhv7cuuzotagythj4 39 24 = = NN work_53xuaunsqfhv7cuuzotagythj4 39 25 φ φ UH work_53xuaunsqfhv7cuuzotagythj4 39 26 , , , work_53xuaunsqfhv7cuuzotagythj4 39 27 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 39 28 Ratio Ratio NNP work_53xuaunsqfhv7cuuzotagythj4 39 29 : : : work_53xuaunsqfhv7cuuzotagythj4 39 30 The the DT work_53xuaunsqfhv7cuuzotagythj4 39 31 Mathematics Mathematics NNPS work_53xuaunsqfhv7cuuzotagythj4 39 32 of of IN work_53xuaunsqfhv7cuuzotagythj4 39 33 Beauty Beauty NNP work_53xuaunsqfhv7cuuzotagythj4 39 34 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 39 35 or or CC work_53xuaunsqfhv7cuuzotagythj4 39 36 φ2 φ2 NN work_53xuaunsqfhv7cuuzotagythj4 39 37 − − NNP work_53xuaunsqfhv7cuuzotagythj4 39 38 φ φ SYM work_53xuaunsqfhv7cuuzotagythj4 39 39 − − NNP work_53xuaunsqfhv7cuuzotagythj4 39 40 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 39 41 = = SYM work_53xuaunsqfhv7cuuzotagythj4 39 42 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 39 43 , , , work_53xuaunsqfhv7cuuzotagythj4 39 44 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 39 45 1 1 LS work_53xuaunsqfhv7cuuzotagythj4 39 46 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 39 47 where where WRB work_53xuaunsqfhv7cuuzotagythj4 39 48 , , , work_53xuaunsqfhv7cuuzotagythj4 39 49 the the DT work_53xuaunsqfhv7cuuzotagythj4 39 50 Greek greek JJ work_53xuaunsqfhv7cuuzotagythj4 39 51 letter letter NN work_53xuaunsqfhv7cuuzotagythj4 39 52 phi phi NN work_53xuaunsqfhv7cuuzotagythj4 39 53 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 39 54 φ φ NNP work_53xuaunsqfhv7cuuzotagythj4 39 55 or or CC work_53xuaunsqfhv7cuuzotagythj4 39 56 ϕ ϕ NN work_53xuaunsqfhv7cuuzotagythj4 39 57 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 39 58 represents represent VBZ work_53xuaunsqfhv7cuuzotagythj4 39 59 the the DT work_53xuaunsqfhv7cuuzotagythj4 39 60 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 39 61 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 39 62 . . . work_53xuaunsqfhv7cuuzotagythj4 40 1 It -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 40 2 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 40 3 an an DT work_53xuaunsqfhv7cuuzotagythj4 40 4 irrational irrational JJ work_53xuaunsqfhv7cuuzotagythj4 40 5 number number NN work_53xuaunsqfhv7cuuzotagythj4 40 6 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 40 7 meaning mean VBG work_53xuaunsqfhv7cuuzotagythj4 40 8 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 40 9 can can MD work_53xuaunsqfhv7cuuzotagythj4 40 10 not not RB work_53xuaunsqfhv7cuuzotagythj4 40 11 write write VB work_53xuaunsqfhv7cuuzotagythj4 40 12 it -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 40 13 as as IN work_53xuaunsqfhv7cuuzotagythj4 40 14 a a DT work_53xuaunsqfhv7cuuzotagythj4 40 15 simple simple JJ work_53xuaunsqfhv7cuuzotagythj4 40 16 fraction fraction NN work_53xuaunsqfhv7cuuzotagythj4 40 17 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 40 18 , , , work_53xuaunsqfhv7cuuzotagythj4 40 19 with with IN work_53xuaunsqfhv7cuuzotagythj4 40 20 a a DT work_53xuaunsqfhv7cuuzotagythj4 40 21 value value NN work_53xuaunsqfhv7cuuzotagythj4 40 22 of of IN work_53xuaunsqfhv7cuuzotagythj4 40 23 : : : work_53xuaunsqfhv7cuuzotagythj4 40 24 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 40 25 = = SYM work_53xuaunsqfhv7cuuzotagythj4 40 26 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 40 27 + + SYM work_53xuaunsqfhv7cuuzotagythj4 40 28 √ √ NN work_53xuaunsqfhv7cuuzotagythj4 40 29 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 40 30 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 40 31 ≈ ≈ NNP work_53xuaunsqfhv7cuuzotagythj4 40 32 1.6180339887 1.6180339887 CD work_53xuaunsqfhv7cuuzotagythj4 40 33 . . . work_53xuaunsqfhv7cuuzotagythj4 41 1 Another another DT work_53xuaunsqfhv7cuuzotagythj4 41 2 interesting interesting JJ work_53xuaunsqfhv7cuuzotagythj4 41 3 relationship relationship NN work_53xuaunsqfhv7cuuzotagythj4 41 4 involving involve VBG work_53xuaunsqfhv7cuuzotagythj4 41 5 the the DT work_53xuaunsqfhv7cuuzotagythj4 41 6 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 41 7 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 41 8 may may MD work_53xuaunsqfhv7cuuzotagythj4 41 9 be be VB work_53xuaunsqfhv7cuuzotagythj4 41 10 obtained obtain VBN work_53xuaunsqfhv7cuuzotagythj4 41 11 di- di- RB work_53xuaunsqfhv7cuuzotagythj4 41 12 rectly rectly RB work_53xuaunsqfhv7cuuzotagythj4 41 13 from from IN work_53xuaunsqfhv7cuuzotagythj4 41 14 : : : work_53xuaunsqfhv7cuuzotagythj4 41 15 φ φ LS work_53xuaunsqfhv7cuuzotagythj4 41 16 = = SYM work_53xuaunsqfhv7cuuzotagythj4 41 17 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 41 18 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 41 19 + + CC work_53xuaunsqfhv7cuuzotagythj4 41 20 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 41 21 , , , work_53xuaunsqfhv7cuuzotagythj4 41 22 successive successive JJ work_53xuaunsqfhv7cuuzotagythj4 41 23 substituting substitute VBG work_53xuaunsqfhv7cuuzotagythj4 41 24 the the DT work_53xuaunsqfhv7cuuzotagythj4 41 25 left left JJ work_53xuaunsqfhv7cuuzotagythj4 41 26 hand hand NN work_53xuaunsqfhv7cuuzotagythj4 41 27 side side NN work_53xuaunsqfhv7cuuzotagythj4 41 28 for for IN work_53xuaunsqfhv7cuuzotagythj4 41 29 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 41 30 on on IN work_53xuaunsqfhv7cuuzotagythj4 41 31 the the DT work_53xuaunsqfhv7cuuzotagythj4 41 32 right right JJ work_53xuaunsqfhv7cuuzotagythj4 41 33 hand hand NN work_53xuaunsqfhv7cuuzotagythj4 41 34 side side NN work_53xuaunsqfhv7cuuzotagythj4 41 35 gives give VBZ work_53xuaunsqfhv7cuuzotagythj4 41 36 : : : work_53xuaunsqfhv7cuuzotagythj4 41 37 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 41 38 = = SYM work_53xuaunsqfhv7cuuzotagythj4 41 39 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 41 40 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 41 41 + + CC work_53xuaunsqfhv7cuuzotagythj4 41 42 √ √ NN work_53xuaunsqfhv7cuuzotagythj4 41 43 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 41 44 + + CC work_53xuaunsqfhv7cuuzotagythj4 41 45 √ √ NN work_53xuaunsqfhv7cuuzotagythj4 41 46 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 41 47 + + SYM work_53xuaunsqfhv7cuuzotagythj4 41 48 · · NFP work_53xuaunsqfhv7cuuzotagythj4 41 49 · · NFP work_53xuaunsqfhv7cuuzotagythj4 41 50 · · NFP work_53xuaunsqfhv7cuuzotagythj4 41 51 . . . work_53xuaunsqfhv7cuuzotagythj4 42 1 Similarly similarly RB work_53xuaunsqfhv7cuuzotagythj4 42 2 , , , work_53xuaunsqfhv7cuuzotagythj4 42 3 replacing replace VBG work_53xuaunsqfhv7cuuzotagythj4 42 4 x x SYM work_53xuaunsqfhv7cuuzotagythj4 42 5 = = SYM work_53xuaunsqfhv7cuuzotagythj4 42 6 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 7 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 42 8 in in IN work_53xuaunsqfhv7cuuzotagythj4 42 9 the the DT work_53xuaunsqfhv7cuuzotagythj4 42 10 equation equation NN work_53xuaunsqfhv7cuuzotagythj4 42 11 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 42 12 1 1 LS work_53xuaunsqfhv7cuuzotagythj4 42 13 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 42 14 yields yield VBZ work_53xuaunsqfhv7cuuzotagythj4 42 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 42 16 quadratic quadratic JJ work_53xuaunsqfhv7cuuzotagythj4 42 17 equation equation NN work_53xuaunsqfhv7cuuzotagythj4 42 18 x2 x2 NNP work_53xuaunsqfhv7cuuzotagythj4 42 19 + + CC work_53xuaunsqfhv7cuuzotagythj4 42 20 x x SYM work_53xuaunsqfhv7cuuzotagythj4 42 21 − − NNP work_53xuaunsqfhv7cuuzotagythj4 42 22 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 23 = = SYM work_53xuaunsqfhv7cuuzotagythj4 42 24 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 42 25 , , , work_53xuaunsqfhv7cuuzotagythj4 42 26 which which WDT work_53xuaunsqfhv7cuuzotagythj4 42 27 its -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 42 28 positive positive JJ work_53xuaunsqfhv7cuuzotagythj4 42 29 root root NN work_53xuaunsqfhv7cuuzotagythj4 42 30 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 42 31 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 32 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 42 33 , , , work_53xuaunsqfhv7cuuzotagythj4 42 34 i.e. i.e. FW work_53xuaunsqfhv7cuuzotagythj4 42 35 , , , work_53xuaunsqfhv7cuuzotagythj4 42 36 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 37 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 42 38 = = SYM work_53xuaunsqfhv7cuuzotagythj4 42 39 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 42 40 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 41 − − NNP work_53xuaunsqfhv7cuuzotagythj4 42 42 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 43 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 42 44 = = SYM work_53xuaunsqfhv7cuuzotagythj4 42 45 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 42 46 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 47 − − NNP work_53xuaunsqfhv7cuuzotagythj4 42 48 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 42 49 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 50 − − NNP work_53xuaunsqfhv7cuuzotagythj4 42 51 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 42 52 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 42 53 − − NNP work_53xuaunsqfhv7cuuzotagythj4 42 54 · · NFP work_53xuaunsqfhv7cuuzotagythj4 42 55 · · NFP work_53xuaunsqfhv7cuuzotagythj4 42 56 · · NFP work_53xuaunsqfhv7cuuzotagythj4 42 57 . . . work_53xuaunsqfhv7cuuzotagythj4 43 1 Again again RB work_53xuaunsqfhv7cuuzotagythj4 43 2 , , , work_53xuaunsqfhv7cuuzotagythj4 43 3 another another DT work_53xuaunsqfhv7cuuzotagythj4 43 4 relationship relationship NN work_53xuaunsqfhv7cuuzotagythj4 43 5 may may MD work_53xuaunsqfhv7cuuzotagythj4 43 6 be be VB work_53xuaunsqfhv7cuuzotagythj4 43 7 obtained obtain VBN work_53xuaunsqfhv7cuuzotagythj4 43 8 , , , work_53xuaunsqfhv7cuuzotagythj4 43 9 by by IN work_53xuaunsqfhv7cuuzotagythj4 43 10 using use VBG work_53xuaunsqfhv7cuuzotagythj4 43 11 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 43 12 = = SYM work_53xuaunsqfhv7cuuzotagythj4 43 13 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 14 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 15 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 16 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 43 17 = = SYM work_53xuaunsqfhv7cuuzotagythj4 43 18 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 19 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 20 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 21 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 22 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 23 11 11 CD work_53xuaunsqfhv7cuuzotagythj4 43 24 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 43 25 = = SYM work_53xuaunsqfhv7cuuzotagythj4 43 26 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 27 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 28 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 29 repeatedly repeatedly RB work_53xuaunsqfhv7cuuzotagythj4 43 30 , , , work_53xuaunsqfhv7cuuzotagythj4 43 31 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 43 32 find find VBP work_53xuaunsqfhv7cuuzotagythj4 43 33 that that DT work_53xuaunsqfhv7cuuzotagythj4 43 34 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 43 35 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 43 36 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 43 37 related relate VBN work_53xuaunsqfhv7cuuzotagythj4 43 38 with with IN work_53xuaunsqfhv7cuuzotagythj4 43 39 the the DT work_53xuaunsqfhv7cuuzotagythj4 43 40 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 43 41 continued continued JJ work_53xuaunsqfhv7cuuzotagythj4 43 42 fraction fraction NN work_53xuaunsqfhv7cuuzotagythj4 43 43 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 43 44 = = SYM work_53xuaunsqfhv7cuuzotagythj4 43 45 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 46 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 47 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 48 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 49 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 50 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 51 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 52 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 53 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 54 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 55 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 56 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 57 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 43 58 + + SYM work_53xuaunsqfhv7cuuzotagythj4 43 59 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 60 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 61 · · NFP work_53xuaunsqfhv7cuuzotagythj4 43 62 . . . work_53xuaunsqfhv7cuuzotagythj4 44 1 Also also RB work_53xuaunsqfhv7cuuzotagythj4 44 2 , , , work_53xuaunsqfhv7cuuzotagythj4 44 3 any any DT work_53xuaunsqfhv7cuuzotagythj4 44 4 power power NN work_53xuaunsqfhv7cuuzotagythj4 44 5 of of IN work_53xuaunsqfhv7cuuzotagythj4 44 6 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 44 7 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 44 8 equal equal JJ work_53xuaunsqfhv7cuuzotagythj4 44 9 to to IN work_53xuaunsqfhv7cuuzotagythj4 44 10 the the DT work_53xuaunsqfhv7cuuzotagythj4 44 11 sum sum NN work_53xuaunsqfhv7cuuzotagythj4 44 12 of of IN work_53xuaunsqfhv7cuuzotagythj4 44 13 the the DT work_53xuaunsqfhv7cuuzotagythj4 44 14 two two CD work_53xuaunsqfhv7cuuzotagythj4 44 15 immediately immediately RB work_53xuaunsqfhv7cuuzotagythj4 44 16 preceding precede VBG work_53xuaunsqfhv7cuuzotagythj4 44 17 powers power NNS work_53xuaunsqfhv7cuuzotagythj4 44 18 : : : work_53xuaunsqfhv7cuuzotagythj4 44 19 φn φn NNP work_53xuaunsqfhv7cuuzotagythj4 44 20 = = SYM work_53xuaunsqfhv7cuuzotagythj4 44 21 φn−1 φn−1 NNP work_53xuaunsqfhv7cuuzotagythj4 44 22 + + NNP work_53xuaunsqfhv7cuuzotagythj4 44 23 φn−2 φn−2 NNP work_53xuaunsqfhv7cuuzotagythj4 44 24 , , , work_53xuaunsqfhv7cuuzotagythj4 44 25 thus thus RB work_53xuaunsqfhv7cuuzotagythj4 44 26 , , , work_53xuaunsqfhv7cuuzotagythj4 44 27 from from IN work_53xuaunsqfhv7cuuzotagythj4 44 28 computation computation NN work_53xuaunsqfhv7cuuzotagythj4 44 29 cost cost NN work_53xuaunsqfhv7cuuzotagythj4 44 30 point point NN work_53xuaunsqfhv7cuuzotagythj4 44 31 of of IN work_53xuaunsqfhv7cuuzotagythj4 44 32 view view NN work_53xuaunsqfhv7cuuzotagythj4 44 33 , , , work_53xuaunsqfhv7cuuzotagythj4 44 34 having have VBG work_53xuaunsqfhv7cuuzotagythj4 44 35 the the DT work_53xuaunsqfhv7cuuzotagythj4 44 36 first first JJ work_53xuaunsqfhv7cuuzotagythj4 44 37 two two CD work_53xuaunsqfhv7cuuzotagythj4 44 38 values value NNS work_53xuaunsqfhv7cuuzotagythj4 44 39 φ0 φ0 VBP work_53xuaunsqfhv7cuuzotagythj4 44 40 = = SYM work_53xuaunsqfhv7cuuzotagythj4 44 41 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 44 42 and and CC work_53xuaunsqfhv7cuuzotagythj4 44 43 φ1 φ1 NNP work_53xuaunsqfhv7cuuzotagythj4 44 44 ≈ ≈ NNP work_53xuaunsqfhv7cuuzotagythj4 44 45 1.61803398 1.61803398 CD work_53xuaunsqfhv7cuuzotagythj4 44 46 , , , work_53xuaunsqfhv7cuuzotagythj4 44 47 for for IN work_53xuaunsqfhv7cuuzotagythj4 44 48 calculating calculate VBG work_53xuaunsqfhv7cuuzotagythj4 44 49 φn φn NN work_53xuaunsqfhv7cuuzotagythj4 44 50 approximately approximately RB work_53xuaunsqfhv7cuuzotagythj4 44 51 , , , work_53xuaunsqfhv7cuuzotagythj4 44 52 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 44 53 can can MD work_53xuaunsqfhv7cuuzotagythj4 44 54 repeatedly repeatedly RB work_53xuaunsqfhv7cuuzotagythj4 44 55 apply apply VB work_53xuaunsqfhv7cuuzotagythj4 44 56 above above IN work_53xuaunsqfhv7cuuzotagythj4 44 57 recursion recursion NN work_53xuaunsqfhv7cuuzotagythj4 44 58 relation relation NN work_53xuaunsqfhv7cuuzotagythj4 44 59 doing do VBG work_53xuaunsqfhv7cuuzotagythj4 44 60 only only RB work_53xuaunsqfhv7cuuzotagythj4 44 61 a a DT work_53xuaunsqfhv7cuuzotagythj4 44 62 single single JJ work_53xuaunsqfhv7cuuzotagythj4 44 63 subtraction subtraction NN work_53xuaunsqfhv7cuuzotagythj4 44 64 , , , work_53xuaunsqfhv7cuuzotagythj4 44 65 rather rather RB work_53xuaunsqfhv7cuuzotagythj4 44 66 than than IN work_53xuaunsqfhv7cuuzotagythj4 44 67 a a DT work_53xuaunsqfhv7cuuzotagythj4 44 68 slower slow JJR work_53xuaunsqfhv7cuuzotagythj4 44 69 multiplication multiplication NN work_53xuaunsqfhv7cuuzotagythj4 44 70 by by IN work_53xuaunsqfhv7cuuzotagythj4 44 71 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 44 72 , , , work_53xuaunsqfhv7cuuzotagythj4 44 73 at at IN work_53xuaunsqfhv7cuuzotagythj4 44 74 each each DT work_53xuaunsqfhv7cuuzotagythj4 44 75 step step NN work_53xuaunsqfhv7cuuzotagythj4 44 76 . . . work_53xuaunsqfhv7cuuzotagythj4 45 1 3.1 3.1 CD work_53xuaunsqfhv7cuuzotagythj4 45 2 The the DT work_53xuaunsqfhv7cuuzotagythj4 45 3 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 45 4 Triangle Triangle NNP work_53xuaunsqfhv7cuuzotagythj4 45 5 A a DT work_53xuaunsqfhv7cuuzotagythj4 45 6 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 45 7 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 45 8 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 45 9 a a DT work_53xuaunsqfhv7cuuzotagythj4 45 10 right right JJ work_53xuaunsqfhv7cuuzotagythj4 45 11 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 45 12 with with IN work_53xuaunsqfhv7cuuzotagythj4 45 13 edge edge NN work_53xuaunsqfhv7cuuzotagythj4 45 14 lengths length NNS work_53xuaunsqfhv7cuuzotagythj4 45 15 in in IN work_53xuaunsqfhv7cuuzotagythj4 45 16 geometric geometric JJ work_53xuaunsqfhv7cuuzotagythj4 45 17 progression progression NN work_53xuaunsqfhv7cuuzotagythj4 45 18 . . . work_53xuaunsqfhv7cuuzotagythj4 46 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 46 2 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 46 3 of of IN work_53xuaunsqfhv7cuuzotagythj4 46 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 46 5 edges edge NNS work_53xuaunsqfhv7cuuzotagythj4 46 6 of of IN work_53xuaunsqfhv7cuuzotagythj4 46 7 a a DT work_53xuaunsqfhv7cuuzotagythj4 46 8 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 46 9 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 46 10 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 46 11 linked link VBN work_53xuaunsqfhv7cuuzotagythj4 46 12 to to IN work_53xuaunsqfhv7cuuzotagythj4 46 13 the the DT work_53xuaunsqfhv7cuuzotagythj4 46 14 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 46 15 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 46 16 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 46 17 = = SYM work_53xuaunsqfhv7cuuzotagythj4 46 18 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 46 19 + + SYM work_53xuaunsqfhv7cuuzotagythj4 46 20 √ √ NN work_53xuaunsqfhv7cuuzotagythj4 46 21 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 46 22 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 46 23 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 46 24 Hamid Hamid NNP work_53xuaunsqfhv7cuuzotagythj4 46 25 Ghorbani Ghorbani NNP work_53xuaunsqfhv7cuuzotagythj4 46 26 and and CC work_53xuaunsqfhv7cuuzotagythj4 46 27 can can MD work_53xuaunsqfhv7cuuzotagythj4 46 28 be be VB work_53xuaunsqfhv7cuuzotagythj4 46 29 written write VBN work_53xuaunsqfhv7cuuzotagythj4 46 30 : : : work_53xuaunsqfhv7cuuzotagythj4 46 31 1 1 LS work_53xuaunsqfhv7cuuzotagythj4 46 32 : : : work_53xuaunsqfhv7cuuzotagythj4 46 33 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 46 34 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 46 35 : : : work_53xuaunsqfhv7cuuzotagythj4 46 36 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 46 37 , , , work_53xuaunsqfhv7cuuzotagythj4 46 38 or or CC work_53xuaunsqfhv7cuuzotagythj4 46 39 approximately approximately RB work_53xuaunsqfhv7cuuzotagythj4 46 40 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 46 41 : : : work_53xuaunsqfhv7cuuzotagythj4 46 42 1.272 1.272 CD work_53xuaunsqfhv7cuuzotagythj4 46 43 : : : work_53xuaunsqfhv7cuuzotagythj4 46 44 1.618 1.618 CD work_53xuaunsqfhv7cuuzotagythj4 46 45 . . . work_53xuaunsqfhv7cuuzotagythj4 47 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 47 2 squares square NNS work_53xuaunsqfhv7cuuzotagythj4 47 3 of of IN work_53xuaunsqfhv7cuuzotagythj4 47 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 47 5 edges edge NNS work_53xuaunsqfhv7cuuzotagythj4 47 6 of of IN work_53xuaunsqfhv7cuuzotagythj4 47 7 this this DT work_53xuaunsqfhv7cuuzotagythj4 47 8 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 47 9 are be VBP work_53xuaunsqfhv7cuuzotagythj4 47 10 in in IN work_53xuaunsqfhv7cuuzotagythj4 47 11 geometric geometric JJ work_53xuaunsqfhv7cuuzotagythj4 47 12 progression progression NN work_53xuaunsqfhv7cuuzotagythj4 47 13 according accord VBG work_53xuaunsqfhv7cuuzotagythj4 47 14 to to IN work_53xuaunsqfhv7cuuzotagythj4 47 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 47 16 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 47 17 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 47 18 . . . work_53xuaunsqfhv7cuuzotagythj4 48 1 Triangles triangle NNS work_53xuaunsqfhv7cuuzotagythj4 48 2 with with IN work_53xuaunsqfhv7cuuzotagythj4 48 3 such such JJ work_53xuaunsqfhv7cuuzotagythj4 48 4 ratios ratio NNS work_53xuaunsqfhv7cuuzotagythj4 48 5 are be VBP work_53xuaunsqfhv7cuuzotagythj4 48 6 named name VBN work_53xuaunsqfhv7cuuzotagythj4 48 7 after after IN work_53xuaunsqfhv7cuuzotagythj4 48 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 48 9 German german JJ work_53xuaunsqfhv7cuuzotagythj4 48 10 math- math- NN work_53xuaunsqfhv7cuuzotagythj4 48 11 ematician ematician NN work_53xuaunsqfhv7cuuzotagythj4 48 12 and and CC work_53xuaunsqfhv7cuuzotagythj4 48 13 astronomer astronomer NN work_53xuaunsqfhv7cuuzotagythj4 48 14 Johannes Johannes NNP work_53xuaunsqfhv7cuuzotagythj4 48 15 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 48 16 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 48 17 1571 1571 CD work_53xuaunsqfhv7cuuzotagythj4 48 18 - - SYM work_53xuaunsqfhv7cuuzotagythj4 48 19 1630 1630 CD work_53xuaunsqfhv7cuuzotagythj4 48 20 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 48 21 , , , work_53xuaunsqfhv7cuuzotagythj4 48 22 who who WP work_53xuaunsqfhv7cuuzotagythj4 48 23 first first RB work_53xuaunsqfhv7cuuzotagythj4 48 24 demonstrated demonstrate VBD work_53xuaunsqfhv7cuuzotagythj4 48 25 that that IN work_53xuaunsqfhv7cuuzotagythj4 48 26 this this DT work_53xuaunsqfhv7cuuzotagythj4 48 27 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 48 28 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 48 29 characterized characterize VBN work_53xuaunsqfhv7cuuzotagythj4 48 30 by by IN work_53xuaunsqfhv7cuuzotagythj4 48 31 a a DT work_53xuaunsqfhv7cuuzotagythj4 48 32 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 48 33 between between IN work_53xuaunsqfhv7cuuzotagythj4 48 34 short short JJ work_53xuaunsqfhv7cuuzotagythj4 48 35 side side NN work_53xuaunsqfhv7cuuzotagythj4 48 36 and and CC work_53xuaunsqfhv7cuuzotagythj4 48 37 hypotenuse hypotenuse VB work_53xuaunsqfhv7cuuzotagythj4 48 38 equal equal JJ work_53xuaunsqfhv7cuuzotagythj4 48 39 to to IN work_53xuaunsqfhv7cuuzotagythj4 48 40 the the DT work_53xuaunsqfhv7cuuzotagythj4 48 41 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 48 42 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 48 43 . . . work_53xuaunsqfhv7cuuzotagythj4 49 1 Kepler kepler NN work_53xuaunsqfhv7cuuzotagythj4 49 2 triangles triangle NNS work_53xuaunsqfhv7cuuzotagythj4 49 3 combine combine VBP work_53xuaunsqfhv7cuuzotagythj4 49 4 two two CD work_53xuaunsqfhv7cuuzotagythj4 49 5 key key JJ work_53xuaunsqfhv7cuuzotagythj4 49 6 mathematical mathematical JJ work_53xuaunsqfhv7cuuzotagythj4 49 7 concept concept NN work_53xuaunsqfhv7cuuzotagythj4 49 8 , , , work_53xuaunsqfhv7cuuzotagythj4 49 9 the the DT work_53xuaunsqfhv7cuuzotagythj4 49 10 Pythagorean pythagorean JJ work_53xuaunsqfhv7cuuzotagythj4 49 11 theorem theorem NN work_53xuaunsqfhv7cuuzotagythj4 49 12 and and CC work_53xuaunsqfhv7cuuzotagythj4 49 13 the the DT work_53xuaunsqfhv7cuuzotagythj4 49 14 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 49 15 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 49 16 , , , work_53xuaunsqfhv7cuuzotagythj4 49 17 that that IN work_53xuaunsqfhv7cuuzotagythj4 49 18 fascinated fascinate VBN work_53xuaunsqfhv7cuuzotagythj4 49 19 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 49 20 deeply deeply RB work_53xuaunsqfhv7cuuzotagythj4 49 21 , , , work_53xuaunsqfhv7cuuzotagythj4 49 22 as as IN work_53xuaunsqfhv7cuuzotagythj4 49 23 he -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 49 24 expressed express VBD work_53xuaunsqfhv7cuuzotagythj4 49 25 in in IN work_53xuaunsqfhv7cuuzotagythj4 49 26 this this DT work_53xuaunsqfhv7cuuzotagythj4 49 27 quotation quotation NN work_53xuaunsqfhv7cuuzotagythj4 49 28 by by IN work_53xuaunsqfhv7cuuzotagythj4 49 29 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 49 30 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 49 31 6 6 CD work_53xuaunsqfhv7cuuzotagythj4 49 32 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 49 33 : : : work_53xuaunsqfhv7cuuzotagythj4 49 34 “ " `` work_53xuaunsqfhv7cuuzotagythj4 49 35 Geometry Geometry NNP work_53xuaunsqfhv7cuuzotagythj4 49 36 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 49 37 two two CD work_53xuaunsqfhv7cuuzotagythj4 49 38 great great JJ work_53xuaunsqfhv7cuuzotagythj4 49 39 treasures treasure NNS work_53xuaunsqfhv7cuuzotagythj4 49 40 : : : work_53xuaunsqfhv7cuuzotagythj4 49 41 one one CD work_53xuaunsqfhv7cuuzotagythj4 49 42 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 49 43 the the DT work_53xuaunsqfhv7cuuzotagythj4 49 44 theorem theorem NN work_53xuaunsqfhv7cuuzotagythj4 49 45 of of IN work_53xuaunsqfhv7cuuzotagythj4 49 46 Pythagoras Pythagoras NNP work_53xuaunsqfhv7cuuzotagythj4 49 47 , , , work_53xuaunsqfhv7cuuzotagythj4 49 48 the the DT work_53xuaunsqfhv7cuuzotagythj4 49 49 other other JJ work_53xuaunsqfhv7cuuzotagythj4 49 50 the the DT work_53xuaunsqfhv7cuuzotagythj4 49 51 division division NN work_53xuaunsqfhv7cuuzotagythj4 49 52 of of IN work_53xuaunsqfhv7cuuzotagythj4 49 53 a a DT work_53xuaunsqfhv7cuuzotagythj4 49 54 line line NN work_53xuaunsqfhv7cuuzotagythj4 49 55 into into IN work_53xuaunsqfhv7cuuzotagythj4 49 56 mean mean JJ work_53xuaunsqfhv7cuuzotagythj4 49 57 and and CC work_53xuaunsqfhv7cuuzotagythj4 49 58 extreme extreme JJ work_53xuaunsqfhv7cuuzotagythj4 49 59 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 49 60 . . . work_53xuaunsqfhv7cuuzotagythj4 50 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 50 2 first first JJ work_53xuaunsqfhv7cuuzotagythj4 50 3 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 50 4 may may MD work_53xuaunsqfhv7cuuzotagythj4 50 5 compare compare VB work_53xuaunsqfhv7cuuzotagythj4 50 6 to to IN work_53xuaunsqfhv7cuuzotagythj4 50 7 a a DT work_53xuaunsqfhv7cuuzotagythj4 50 8 mass mass NN work_53xuaunsqfhv7cuuzotagythj4 50 9 of of IN work_53xuaunsqfhv7cuuzotagythj4 50 10 gold gold NN work_53xuaunsqfhv7cuuzotagythj4 50 11 , , , work_53xuaunsqfhv7cuuzotagythj4 50 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 50 13 second second JJ work_53xuaunsqfhv7cuuzotagythj4 50 14 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 50 15 may may MD work_53xuaunsqfhv7cuuzotagythj4 50 16 call call VB work_53xuaunsqfhv7cuuzotagythj4 50 17 a a DT work_53xuaunsqfhv7cuuzotagythj4 50 18 precious precious JJ work_53xuaunsqfhv7cuuzotagythj4 50 19 jewel jewel NN work_53xuaunsqfhv7cuuzotagythj4 50 20 ” " '' work_53xuaunsqfhv7cuuzotagythj4 50 21 . . . work_53xuaunsqfhv7cuuzotagythj4 51 1 Some some DT work_53xuaunsqfhv7cuuzotagythj4 51 2 sources source NNS work_53xuaunsqfhv7cuuzotagythj4 51 3 claim claim VBP work_53xuaunsqfhv7cuuzotagythj4 51 4 that that IN work_53xuaunsqfhv7cuuzotagythj4 51 5 a a DT work_53xuaunsqfhv7cuuzotagythj4 51 6 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 51 7 with with IN work_53xuaunsqfhv7cuuzotagythj4 51 8 dimensions dimension NNS work_53xuaunsqfhv7cuuzotagythj4 51 9 closely closely RB work_53xuaunsqfhv7cuuzotagythj4 51 10 approximating approximate VBG work_53xuaunsqfhv7cuuzotagythj4 51 11 a a DT work_53xuaunsqfhv7cuuzotagythj4 51 12 Kepler Kepler NNP work_53xuaunsqfhv7cuuzotagythj4 51 13 triangle triangle NN work_53xuaunsqfhv7cuuzotagythj4 51 14 can can MD work_53xuaunsqfhv7cuuzotagythj4 51 15 be be VB work_53xuaunsqfhv7cuuzotagythj4 51 16 recognized recognize VBN work_53xuaunsqfhv7cuuzotagythj4 51 17 in in IN work_53xuaunsqfhv7cuuzotagythj4 51 18 the the DT work_53xuaunsqfhv7cuuzotagythj4 51 19 Great Great NNP work_53xuaunsqfhv7cuuzotagythj4 51 20 Pyramid Pyramid NNP work_53xuaunsqfhv7cuuzotagythj4 51 21 of of IN work_53xuaunsqfhv7cuuzotagythj4 51 22 Giza Giza NNP work_53xuaunsqfhv7cuuzotagythj4 51 23 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 51 24 7 7 CD work_53xuaunsqfhv7cuuzotagythj4 51 25 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 51 26 . . . work_53xuaunsqfhv7cuuzotagythj4 52 1 3.2 3.2 CD work_53xuaunsqfhv7cuuzotagythj4 52 2 The the DT work_53xuaunsqfhv7cuuzotagythj4 52 3 Fibonacci fibonacci JJ work_53xuaunsqfhv7cuuzotagythj4 52 4 Sequence Sequence NNP work_53xuaunsqfhv7cuuzotagythj4 52 5 The the DT work_53xuaunsqfhv7cuuzotagythj4 52 6 Fibonacci Fibonacci NNP work_53xuaunsqfhv7cuuzotagythj4 52 7 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 52 8 , , , work_53xuaunsqfhv7cuuzotagythj4 52 9 named name VBN work_53xuaunsqfhv7cuuzotagythj4 52 10 after after IN work_53xuaunsqfhv7cuuzotagythj4 52 11 Leonardo Leonardo NNP work_53xuaunsqfhv7cuuzotagythj4 52 12 Fibonacci Fibonacci NNP work_53xuaunsqfhv7cuuzotagythj4 52 13 an an DT work_53xuaunsqfhv7cuuzotagythj4 52 14 Italian Italian NNP work_53xuaunsqfhv7cuuzotagythj4 52 15 born bear VBN work_53xuaunsqfhv7cuuzotagythj4 52 16 in in IN work_53xuaunsqfhv7cuuzotagythj4 52 17 1175 1175 CD work_53xuaunsqfhv7cuuzotagythj4 52 18 AD ad NN work_53xuaunsqfhv7cuuzotagythj4 52 19 , , , work_53xuaunsqfhv7cuuzotagythj4 52 20 also also RB work_53xuaunsqfhv7cuuzotagythj4 52 21 a a DT work_53xuaunsqfhv7cuuzotagythj4 52 22 plot plot NN work_53xuaunsqfhv7cuuzotagythj4 52 23 element element NN work_53xuaunsqfhv7cuuzotagythj4 52 24 in in IN work_53xuaunsqfhv7cuuzotagythj4 52 25 “ " `` work_53xuaunsqfhv7cuuzotagythj4 52 26 The the DT work_53xuaunsqfhv7cuuzotagythj4 52 27 Da Da NNP work_53xuaunsqfhv7cuuzotagythj4 52 28 Vinci Vinci NNP work_53xuaunsqfhv7cuuzotagythj4 52 29 Code Code NNP work_53xuaunsqfhv7cuuzotagythj4 52 30 , , , work_53xuaunsqfhv7cuuzotagythj4 52 31 provides provide VBZ work_53xuaunsqfhv7cuuzotagythj4 52 32 yet yet RB work_53xuaunsqfhv7cuuzotagythj4 52 33 another another DT work_53xuaunsqfhv7cuuzotagythj4 52 34 way way NN work_53xuaunsqfhv7cuuzotagythj4 52 35 to to TO work_53xuaunsqfhv7cuuzotagythj4 52 36 derive derive VB work_53xuaunsqfhv7cuuzotagythj4 52 37 Phi Phi NNP work_53xuaunsqfhv7cuuzotagythj4 52 38 mathematically mathematically RB work_53xuaunsqfhv7cuuzotagythj4 52 39 . . . work_53xuaunsqfhv7cuuzotagythj4 53 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 53 2 series series NN work_53xuaunsqfhv7cuuzotagythj4 53 3 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 53 4 quite quite RB work_53xuaunsqfhv7cuuzotagythj4 53 5 simple simple JJ work_53xuaunsqfhv7cuuzotagythj4 53 6 . . . work_53xuaunsqfhv7cuuzotagythj4 54 1 Start start VB work_53xuaunsqfhv7cuuzotagythj4 54 2 with with IN work_53xuaunsqfhv7cuuzotagythj4 54 3 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 54 4 and and CC work_53xuaunsqfhv7cuuzotagythj4 54 5 add add VB work_53xuaunsqfhv7cuuzotagythj4 54 6 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 54 7 to to TO work_53xuaunsqfhv7cuuzotagythj4 54 8 get get VB work_53xuaunsqfhv7cuuzotagythj4 54 9 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 54 10 . . . work_53xuaunsqfhv7cuuzotagythj4 55 1 Then then RB work_53xuaunsqfhv7cuuzotagythj4 55 2 repeat repeat VB work_53xuaunsqfhv7cuuzotagythj4 55 3 the the DT work_53xuaunsqfhv7cuuzotagythj4 55 4 process process NN work_53xuaunsqfhv7cuuzotagythj4 55 5 of of IN work_53xuaunsqfhv7cuuzotagythj4 55 6 adding add VBG work_53xuaunsqfhv7cuuzotagythj4 55 7 each each DT work_53xuaunsqfhv7cuuzotagythj4 55 8 two two CD work_53xuaunsqfhv7cuuzotagythj4 55 9 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 55 10 in in IN work_53xuaunsqfhv7cuuzotagythj4 55 11 the the DT work_53xuaunsqfhv7cuuzotagythj4 55 12 series series NN work_53xuaunsqfhv7cuuzotagythj4 55 13 to to TO work_53xuaunsqfhv7cuuzotagythj4 55 14 determine determine VB work_53xuaunsqfhv7cuuzotagythj4 55 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 55 16 next next JJ work_53xuaunsqfhv7cuuzotagythj4 55 17 one one CD work_53xuaunsqfhv7cuuzotagythj4 55 18 : : : work_53xuaunsqfhv7cuuzotagythj4 55 19 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 55 20 , , , work_53xuaunsqfhv7cuuzotagythj4 55 21 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 55 22 , , , work_53xuaunsqfhv7cuuzotagythj4 55 23 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 55 24 , , , work_53xuaunsqfhv7cuuzotagythj4 55 25 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 55 26 , , , work_53xuaunsqfhv7cuuzotagythj4 55 27 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 55 28 , , , work_53xuaunsqfhv7cuuzotagythj4 55 29 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 55 30 , , , work_53xuaunsqfhv7cuuzotagythj4 55 31 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 55 32 , , , work_53xuaunsqfhv7cuuzotagythj4 55 33 13 13 CD work_53xuaunsqfhv7cuuzotagythj4 55 34 , , , work_53xuaunsqfhv7cuuzotagythj4 55 35 21 21 CD work_53xuaunsqfhv7cuuzotagythj4 55 36 , , , work_53xuaunsqfhv7cuuzotagythj4 55 37 34 34 CD work_53xuaunsqfhv7cuuzotagythj4 55 38 , , , work_53xuaunsqfhv7cuuzotagythj4 55 39 55 55 CD work_53xuaunsqfhv7cuuzotagythj4 55 40 , , , work_53xuaunsqfhv7cuuzotagythj4 55 41 89 89 CD work_53xuaunsqfhv7cuuzotagythj4 55 42 , , , work_53xuaunsqfhv7cuuzotagythj4 55 43 144 144 CD work_53xuaunsqfhv7cuuzotagythj4 55 44 , , , work_53xuaunsqfhv7cuuzotagythj4 55 45 233 233 CD work_53xuaunsqfhv7cuuzotagythj4 55 46 , , , work_53xuaunsqfhv7cuuzotagythj4 55 47 and and CC work_53xuaunsqfhv7cuuzotagythj4 55 48 so so RB work_53xuaunsqfhv7cuuzotagythj4 55 49 on on RB work_53xuaunsqfhv7cuuzotagythj4 55 50 . . . work_53xuaunsqfhv7cuuzotagythj4 56 1 This this DT work_53xuaunsqfhv7cuuzotagythj4 56 2 pattern pattern NN work_53xuaunsqfhv7cuuzotagythj4 56 3 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 56 4 also also RB work_53xuaunsqfhv7cuuzotagythj4 56 5 found find VBN work_53xuaunsqfhv7cuuzotagythj4 56 6 in in IN work_53xuaunsqfhv7cuuzotagythj4 56 7 the the DT work_53xuaunsqfhv7cuuzotagythj4 56 8 diagonals diagonal NNS work_53xuaunsqfhv7cuuzotagythj4 56 9 of of IN work_53xuaunsqfhv7cuuzotagythj4 56 10 Pascals Pascals NNPS work_53xuaunsqfhv7cuuzotagythj4 56 11 Triangle Triangle NNP work_53xuaunsqfhv7cuuzotagythj4 56 12 . . . work_53xuaunsqfhv7cuuzotagythj4 57 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 57 2 relationship relationship NN work_53xuaunsqfhv7cuuzotagythj4 57 3 to to IN work_53xuaunsqfhv7cuuzotagythj4 57 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 57 5 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 57 6 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 57 7 or or CC work_53xuaunsqfhv7cuuzotagythj4 57 8 Phi Phi NNP work_53xuaunsqfhv7cuuzotagythj4 57 9 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 57 10 found find VBN work_53xuaunsqfhv7cuuzotagythj4 57 11 by by IN work_53xuaunsqfhv7cuuzotagythj4 57 12 dividing divide VBG work_53xuaunsqfhv7cuuzotagythj4 57 13 each each DT work_53xuaunsqfhv7cuuzotagythj4 57 14 number number NN work_53xuaunsqfhv7cuuzotagythj4 57 15 by by IN work_53xuaunsqfhv7cuuzotagythj4 57 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 57 17 one one NN work_53xuaunsqfhv7cuuzotagythj4 57 18 before before IN work_53xuaunsqfhv7cuuzotagythj4 57 19 it -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 57 20 . . . work_53xuaunsqfhv7cuuzotagythj4 58 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 58 2 further far RBR work_53xuaunsqfhv7cuuzotagythj4 58 3 you -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 58 4 go go VBP work_53xuaunsqfhv7cuuzotagythj4 58 5 in in IN work_53xuaunsqfhv7cuuzotagythj4 58 6 the the DT work_53xuaunsqfhv7cuuzotagythj4 58 7 series series NN work_53xuaunsqfhv7cuuzotagythj4 58 8 , , , work_53xuaunsqfhv7cuuzotagythj4 58 9 the the DT work_53xuaunsqfhv7cuuzotagythj4 58 10 closer close JJR work_53xuaunsqfhv7cuuzotagythj4 58 11 the the DT work_53xuaunsqfhv7cuuzotagythj4 58 12 result result NN work_53xuaunsqfhv7cuuzotagythj4 58 13 gets get VBZ work_53xuaunsqfhv7cuuzotagythj4 58 14 to to IN work_53xuaunsqfhv7cuuzotagythj4 58 15 Phi Phi NNP work_53xuaunsqfhv7cuuzotagythj4 58 16 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 58 17 22 22 CD work_53xuaunsqfhv7cuuzotagythj4 58 18 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 58 19 . . . work_53xuaunsqfhv7cuuzotagythj4 59 1 For for IN work_53xuaunsqfhv7cuuzotagythj4 59 2 example example NN work_53xuaunsqfhv7cuuzotagythj4 59 3 : : : work_53xuaunsqfhv7cuuzotagythj4 59 4 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 59 5 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 59 6 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 7 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 59 8 , , , work_53xuaunsqfhv7cuuzotagythj4 59 9 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 59 10 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 59 11 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 12 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 59 13 , , , work_53xuaunsqfhv7cuuzotagythj4 59 14 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 59 15 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 59 16 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 17 1.5 1.5 CD work_53xuaunsqfhv7cuuzotagythj4 59 18 , , , work_53xuaunsqfhv7cuuzotagythj4 59 19 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 59 20 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 59 21 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 22 1.666 1.666 CD work_53xuaunsqfhv7cuuzotagythj4 59 23 , , , work_53xuaunsqfhv7cuuzotagythj4 59 24 13 13 CD work_53xuaunsqfhv7cuuzotagythj4 59 25 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 59 26 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 27 1.625 1.625 CD work_53xuaunsqfhv7cuuzotagythj4 59 28 , , , work_53xuaunsqfhv7cuuzotagythj4 59 29 21 21 CD work_53xuaunsqfhv7cuuzotagythj4 59 30 13 13 CD work_53xuaunsqfhv7cuuzotagythj4 59 31 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 32 1.615 1.615 CD work_53xuaunsqfhv7cuuzotagythj4 59 33 , , , work_53xuaunsqfhv7cuuzotagythj4 59 34 if if IN work_53xuaunsqfhv7cuuzotagythj4 59 35 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 59 36 go go VBP work_53xuaunsqfhv7cuuzotagythj4 59 37 further further RB work_53xuaunsqfhv7cuuzotagythj4 59 38 into into IN work_53xuaunsqfhv7cuuzotagythj4 59 39 the the DT work_53xuaunsqfhv7cuuzotagythj4 59 40 series series NN work_53xuaunsqfhv7cuuzotagythj4 59 41 , , , work_53xuaunsqfhv7cuuzotagythj4 59 42 it -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 59 43 will will MD work_53xuaunsqfhv7cuuzotagythj4 59 44 find find VB work_53xuaunsqfhv7cuuzotagythj4 59 45 that that IN work_53xuaunsqfhv7cuuzotagythj4 59 46 233 233 CD work_53xuaunsqfhv7cuuzotagythj4 59 47 144 144 CD work_53xuaunsqfhv7cuuzotagythj4 59 48 = = SYM work_53xuaunsqfhv7cuuzotagythj4 59 49 1.61805 1.61805 CD work_53xuaunsqfhv7cuuzotagythj4 59 50 . . . work_53xuaunsqfhv7cuuzotagythj4 60 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 60 2 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 60 3 number number NN work_53xuaunsqfhv7cuuzotagythj4 60 4 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 60 5 not not RB work_53xuaunsqfhv7cuuzotagythj4 60 6 just just RB work_53xuaunsqfhv7cuuzotagythj4 60 7 the the DT work_53xuaunsqfhv7cuuzotagythj4 60 8 limit limit NN work_53xuaunsqfhv7cuuzotagythj4 60 9 of of IN work_53xuaunsqfhv7cuuzotagythj4 60 10 the the DT work_53xuaunsqfhv7cuuzotagythj4 60 11 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 60 12 of of IN work_53xuaunsqfhv7cuuzotagythj4 60 13 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 60 14 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 60 15 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 60 16 , , , work_53xuaunsqfhv7cuuzotagythj4 60 17 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 60 18 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 60 19 , , , work_53xuaunsqfhv7cuuzotagythj4 60 20 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 60 21 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 60 22 , , , work_53xuaunsqfhv7cuuzotagythj4 60 23 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 60 24 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 60 25 , , , work_53xuaunsqfhv7cuuzotagythj4 60 26 ... ... NFP work_53xuaunsqfhv7cuuzotagythj4 60 27 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 60 28 , , , work_53xuaunsqfhv7cuuzotagythj4 60 29 but but CC work_53xuaunsqfhv7cuuzotagythj4 60 30 the the DT work_53xuaunsqfhv7cuuzotagythj4 60 31 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 60 32 of of IN work_53xuaunsqfhv7cuuzotagythj4 60 33 convergent convergent NN work_53xuaunsqfhv7cuuzotagythj4 60 34 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 60 35 a a DT work_53xuaunsqfhv7cuuzotagythj4 60 36 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 60 37 of of IN work_53xuaunsqfhv7cuuzotagythj4 60 38 best good JJS work_53xuaunsqfhv7cuuzotagythj4 60 39 approximations approximation NNS work_53xuaunsqfhv7cuuzotagythj4 60 40 to to IN work_53xuaunsqfhv7cuuzotagythj4 60 41 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 60 42 by by IN work_53xuaunsqfhv7cuuzotagythj4 60 43 rational rational JJ work_53xuaunsqfhv7cuuzotagythj4 60 44 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 60 45 , , , work_53xuaunsqfhv7cuuzotagythj4 60 46 see see VB work_53xuaunsqfhv7cuuzotagythj4 60 47 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 60 48 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 60 49 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 60 50 , , , work_53xuaunsqfhv7cuuzotagythj4 60 51 Chapter chapter NN work_53xuaunsqfhv7cuuzotagythj4 60 52 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 60 53 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 60 54 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 60 55 . . . work_53xuaunsqfhv7cuuzotagythj4 61 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 61 2 relation relation NN work_53xuaunsqfhv7cuuzotagythj4 61 3 between between IN work_53xuaunsqfhv7cuuzotagythj4 61 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 61 5 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 61 6 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 61 7 formula formula NN work_53xuaunsqfhv7cuuzotagythj4 61 8 and and CC work_53xuaunsqfhv7cuuzotagythj4 61 9 Fibonacci fibonacci JJ work_53xuaunsqfhv7cuuzotagythj4 61 10 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 61 11 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 61 12 known know VBN work_53xuaunsqfhv7cuuzotagythj4 61 13 as as IN work_53xuaunsqfhv7cuuzotagythj4 61 14 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 61 15 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 61 16 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 61 17 . . . work_53xuaunsqfhv7cuuzotagythj4 62 1 A a DT work_53xuaunsqfhv7cuuzotagythj4 62 2 Fibonacci fibonacci JJ work_53xuaunsqfhv7cuuzotagythj4 62 3 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 62 4 { { -LRB- work_53xuaunsqfhv7cuuzotagythj4 62 5 an an DT work_53xuaunsqfhv7cuuzotagythj4 62 6 } } -RRB- work_53xuaunsqfhv7cuuzotagythj4 62 7 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 62 8 defined define VBN work_53xuaunsqfhv7cuuzotagythj4 62 9 by by IN work_53xuaunsqfhv7cuuzotagythj4 62 10 second second JJ work_53xuaunsqfhv7cuuzotagythj4 62 11 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 62 12 order order NN work_53xuaunsqfhv7cuuzotagythj4 62 13 linear linear NN work_53xuaunsqfhv7cuuzotagythj4 62 14 dif- dif- CC work_53xuaunsqfhv7cuuzotagythj4 62 15 ference ference NN work_53xuaunsqfhv7cuuzotagythj4 62 16 equation equation NN work_53xuaunsqfhv7cuuzotagythj4 62 17 an+2 an+2 NNP work_53xuaunsqfhv7cuuzotagythj4 62 18 − − NNP work_53xuaunsqfhv7cuuzotagythj4 62 19 an+1 an+1 NNP work_53xuaunsqfhv7cuuzotagythj4 62 20 − − NNP work_53xuaunsqfhv7cuuzotagythj4 62 21 an an DT work_53xuaunsqfhv7cuuzotagythj4 62 22 = = SYM work_53xuaunsqfhv7cuuzotagythj4 62 23 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 62 24 with with IN work_53xuaunsqfhv7cuuzotagythj4 62 25 a0 a0 NN work_53xuaunsqfhv7cuuzotagythj4 62 26 = = SYM work_53xuaunsqfhv7cuuzotagythj4 62 27 0 0 NFP work_53xuaunsqfhv7cuuzotagythj4 62 28 , , , work_53xuaunsqfhv7cuuzotagythj4 62 29 a1 a1 NNP work_53xuaunsqfhv7cuuzotagythj4 62 30 = = SYM work_53xuaunsqfhv7cuuzotagythj4 62 31 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 62 32 , , , work_53xuaunsqfhv7cuuzotagythj4 62 33 then then RB work_53xuaunsqfhv7cuuzotagythj4 62 34 we -PRON- PRP work_53xuaunsqfhv7cuuzotagythj4 62 35 have have VBP work_53xuaunsqfhv7cuuzotagythj4 62 36 the the DT work_53xuaunsqfhv7cuuzotagythj4 62 37 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 62 38 lemma lemma NN work_53xuaunsqfhv7cuuzotagythj4 62 39 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 62 40 13 13 CD work_53xuaunsqfhv7cuuzotagythj4 62 41 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 62 42 . . . work_53xuaunsqfhv7cuuzotagythj4 63 1 Lemma Lemma NNP work_53xuaunsqfhv7cuuzotagythj4 63 2 3.1 3.1 CD work_53xuaunsqfhv7cuuzotagythj4 63 3 . . . work_53xuaunsqfhv7cuuzotagythj4 64 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 64 2 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 64 3 relations relation NNS work_53xuaunsqfhv7cuuzotagythj4 64 4 hold hold VBP work_53xuaunsqfhv7cuuzotagythj4 64 5 : : : work_53xuaunsqfhv7cuuzotagythj4 64 6 φn φn NN work_53xuaunsqfhv7cuuzotagythj4 64 7 = = SYM work_53xuaunsqfhv7cuuzotagythj4 64 8 anφ anφ NN work_53xuaunsqfhv7cuuzotagythj4 64 9 + + SYM work_53xuaunsqfhv7cuuzotagythj4 64 10 an−1 an−1 XX work_53xuaunsqfhv7cuuzotagythj4 64 11 , , , work_53xuaunsqfhv7cuuzotagythj4 64 12 n n NN work_53xuaunsqfhv7cuuzotagythj4 64 13 = = SYM work_53xuaunsqfhv7cuuzotagythj4 64 14 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 15 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 16 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 17 , , , work_53xuaunsqfhv7cuuzotagythj4 64 18 −2 −2 NNP work_53xuaunsqfhv7cuuzotagythj4 64 19 , , , work_53xuaunsqfhv7cuuzotagythj4 64 20 −1 −1 NNP work_53xuaunsqfhv7cuuzotagythj4 64 21 , , , work_53xuaunsqfhv7cuuzotagythj4 64 22 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 64 23 , , , work_53xuaunsqfhv7cuuzotagythj4 64 24 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 64 25 , , , work_53xuaunsqfhv7cuuzotagythj4 64 26 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 64 27 , , , work_53xuaunsqfhv7cuuzotagythj4 64 28 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 29 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 30 · · NFP work_53xuaunsqfhv7cuuzotagythj4 64 31 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 64 32 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 64 33 − − NNP work_53xuaunsqfhv7cuuzotagythj4 64 34 1)n 1)n CD work_53xuaunsqfhv7cuuzotagythj4 64 35 = = SYM work_53xuaunsqfhv7cuuzotagythj4 64 36 a−nφ a−nφ NNP work_53xuaunsqfhv7cuuzotagythj4 64 37 + + SYM work_53xuaunsqfhv7cuuzotagythj4 64 38 a−n−1 a−n−1 NNP work_53xuaunsqfhv7cuuzotagythj4 64 39 . . . work_53xuaunsqfhv7cuuzotagythj4 65 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 65 2 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 65 3 shows show VBZ work_53xuaunsqfhv7cuuzotagythj4 65 4 also also RB work_53xuaunsqfhv7cuuzotagythj4 65 5 that that IN work_53xuaunsqfhv7cuuzotagythj4 65 6 the the DT work_53xuaunsqfhv7cuuzotagythj4 65 7 Fibonacci Fibonacci NNP work_53xuaunsqfhv7cuuzotagythj4 65 8 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 65 9 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 65 10 the the DT work_53xuaunsqfhv7cuuzotagythj4 65 11 analytic analytic JJ work_53xuaunsqfhv7cuuzotagythj4 65 12 form form NN work_53xuaunsqfhv7cuuzotagythj4 65 13 . . . work_53xuaunsqfhv7cuuzotagythj4 66 1 Golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 66 2 Ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 66 3 : : : work_53xuaunsqfhv7cuuzotagythj4 66 4 The the DT work_53xuaunsqfhv7cuuzotagythj4 66 5 Mathematics Mathematics NNPS work_53xuaunsqfhv7cuuzotagythj4 66 6 of of IN work_53xuaunsqfhv7cuuzotagythj4 66 7 Beauty Beauty NNP work_53xuaunsqfhv7cuuzotagythj4 66 8 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 66 9 Lemma Lemma NNP work_53xuaunsqfhv7cuuzotagythj4 66 10 3.2 3.2 CD work_53xuaunsqfhv7cuuzotagythj4 66 11 . . . work_53xuaunsqfhv7cuuzotagythj4 67 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 67 2 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 67 3 relation relation NN work_53xuaunsqfhv7cuuzotagythj4 67 4 holds hold VBZ work_53xuaunsqfhv7cuuzotagythj4 67 5 : : : work_53xuaunsqfhv7cuuzotagythj4 67 6 an an DT work_53xuaunsqfhv7cuuzotagythj4 67 7 = = NN work_53xuaunsqfhv7cuuzotagythj4 67 8 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 67 9 2φ 2φ CD work_53xuaunsqfhv7cuuzotagythj4 67 10 − − NNP work_53xuaunsqfhv7cuuzotagythj4 67 11 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 67 12 { { -LRB- work_53xuaunsqfhv7cuuzotagythj4 67 13 φn φn NN work_53xuaunsqfhv7cuuzotagythj4 67 14 − − NNP work_53xuaunsqfhv7cuuzotagythj4 67 15 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 67 16 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 67 17 − − NNP work_53xuaunsqfhv7cuuzotagythj4 67 18 φ)n φ)n NNP work_53xuaunsqfhv7cuuzotagythj4 67 19 } } -RRB- work_53xuaunsqfhv7cuuzotagythj4 67 20 , , , work_53xuaunsqfhv7cuuzotagythj4 67 21 n n CC work_53xuaunsqfhv7cuuzotagythj4 67 22 = = SYM work_53xuaunsqfhv7cuuzotagythj4 67 23 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 24 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 25 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 26 , , , work_53xuaunsqfhv7cuuzotagythj4 67 27 −2 −2 NNP work_53xuaunsqfhv7cuuzotagythj4 67 28 , , , work_53xuaunsqfhv7cuuzotagythj4 67 29 −1 −1 NNP work_53xuaunsqfhv7cuuzotagythj4 67 30 , , , work_53xuaunsqfhv7cuuzotagythj4 67 31 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 67 32 , , , work_53xuaunsqfhv7cuuzotagythj4 67 33 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 67 34 , , , work_53xuaunsqfhv7cuuzotagythj4 67 35 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 67 36 , , , work_53xuaunsqfhv7cuuzotagythj4 67 37 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 38 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 39 · · NFP work_53xuaunsqfhv7cuuzotagythj4 67 40 . . . work_53xuaunsqfhv7cuuzotagythj4 68 1 Lemma Lemma NNP work_53xuaunsqfhv7cuuzotagythj4 68 2 3.3 3.3 CD work_53xuaunsqfhv7cuuzotagythj4 68 3 . . . work_53xuaunsqfhv7cuuzotagythj4 69 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 69 2 following follow VBG work_53xuaunsqfhv7cuuzotagythj4 69 3 relations relation NNS work_53xuaunsqfhv7cuuzotagythj4 69 4 hold hold VBP work_53xuaunsqfhv7cuuzotagythj4 69 5 : : : work_53xuaunsqfhv7cuuzotagythj4 69 6 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 69 7 i i NN work_53xuaunsqfhv7cuuzotagythj4 69 8 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 69 9 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 69 10 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 11 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 12 1+φ 1+φ CD work_53xuaunsqfhv7cuuzotagythj4 69 13 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 69 14 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 15 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 16 + + SYM work_53xuaunsqfhv7cuuzotagythj4 69 17 2φ 2φ CD work_53xuaunsqfhv7cuuzotagythj4 69 18 1+φ 1+φ CD work_53xuaunsqfhv7cuuzotagythj4 69 19 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 20 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 69 21 + + SYM work_53xuaunsqfhv7cuuzotagythj4 69 22 3φ 3φ CD work_53xuaunsqfhv7cuuzotagythj4 69 23 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 24 + + SYM work_53xuaunsqfhv7cuuzotagythj4 69 25 2φ 2φ CD work_53xuaunsqfhv7cuuzotagythj4 69 26 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 27 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 69 28 + + SYM work_53xuaunsqfhv7cuuzotagythj4 69 29 5φ 5φ CD work_53xuaunsqfhv7cuuzotagythj4 69 30 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 69 31 + + SYM work_53xuaunsqfhv7cuuzotagythj4 69 32 3φ 3φ CD work_53xuaunsqfhv7cuuzotagythj4 69 33 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 34 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 35 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 36 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 37 = = NFP work_53xuaunsqfhv7cuuzotagythj4 69 38 an+an+1φ an+an+1φ NNP work_53xuaunsqfhv7cuuzotagythj4 69 39 an−1+anφ an−1+anφ NNP work_53xuaunsqfhv7cuuzotagythj4 69 40 ≈ ≈ NNP work_53xuaunsqfhv7cuuzotagythj4 69 41 1.61803 1.61803 CD work_53xuaunsqfhv7cuuzotagythj4 69 42 , , , work_53xuaunsqfhv7cuuzotagythj4 69 43 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 69 44 ii ii NN work_53xuaunsqfhv7cuuzotagythj4 69 45 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 69 46 an+an+1φ an+an+1φ NNP work_53xuaunsqfhv7cuuzotagythj4 69 47 an−1+anφ an−1+anφ NNP work_53xuaunsqfhv7cuuzotagythj4 69 48 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 49 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 50 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 51 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 52 = = NFP work_53xuaunsqfhv7cuuzotagythj4 69 53 2φ−3 2φ−3 CD work_53xuaunsqfhv7cuuzotagythj4 69 54 5−3φ 5−3φ CD work_53xuaunsqfhv7cuuzotagythj4 69 55 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 56 2−φ 2−φ CD work_53xuaunsqfhv7cuuzotagythj4 69 57 2φ−3 2φ−3 CD work_53xuaunsqfhv7cuuzotagythj4 69 58 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 59 φ−1 φ−1 NNP work_53xuaunsqfhv7cuuzotagythj4 69 60 2φ 2φ CD work_53xuaunsqfhv7cuuzotagythj4 69 61 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 62 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 63 φ−1 φ−1 NNP work_53xuaunsqfhv7cuuzotagythj4 69 64 = = SYM work_53xuaunsqfhv7cuuzotagythj4 69 65 φ φ NN work_53xuaunsqfhv7cuuzotagythj4 69 66 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 67 , , , work_53xuaunsqfhv7cuuzotagythj4 69 68 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 69 69 iii iii NN work_53xuaunsqfhv7cuuzotagythj4 69 70 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 69 71 0.236 0.236 CD work_53xuaunsqfhv7cuuzotagythj4 69 72 0.146 0.146 CD work_53xuaunsqfhv7cuuzotagythj4 69 73 ≈ ≈ IN work_53xuaunsqfhv7cuuzotagythj4 69 74 0.382 0.382 CD work_53xuaunsqfhv7cuuzotagythj4 69 75 0.236 0.236 CD work_53xuaunsqfhv7cuuzotagythj4 69 76 ≈ ≈ NNS work_53xuaunsqfhv7cuuzotagythj4 69 77 0.618 0.618 CD work_53xuaunsqfhv7cuuzotagythj4 69 78 0.382 0.382 CD work_53xuaunsqfhv7cuuzotagythj4 69 79 ≈ ≈ NN work_53xuaunsqfhv7cuuzotagythj4 69 80 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 81 0.618 0.618 CD work_53xuaunsqfhv7cuuzotagythj4 69 82 ≈ ≈ NN work_53xuaunsqfhv7cuuzotagythj4 69 83 1.618 1.618 CD work_53xuaunsqfhv7cuuzotagythj4 69 84 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 69 85 ≈ ≈ NNS work_53xuaunsqfhv7cuuzotagythj4 69 86 2618 2618 CD work_53xuaunsqfhv7cuuzotagythj4 69 87 1618 1618 CD work_53xuaunsqfhv7cuuzotagythj4 69 88 ≈ ≈ NN work_53xuaunsqfhv7cuuzotagythj4 69 89 4236 4236 CD work_53xuaunsqfhv7cuuzotagythj4 69 90 2618 2618 CD work_53xuaunsqfhv7cuuzotagythj4 69 91 ≈ ≈ NNS work_53xuaunsqfhv7cuuzotagythj4 69 92 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 93 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 94 · · NFP work_53xuaunsqfhv7cuuzotagythj4 69 95 ≈ ≈ RB work_53xuaunsqfhv7cuuzotagythj4 69 96 1.618 1.618 CD work_53xuaunsqfhv7cuuzotagythj4 69 97 . . . work_53xuaunsqfhv7cuuzotagythj4 70 1 3.3 3.3 CD work_53xuaunsqfhv7cuuzotagythj4 70 2 The the DT work_53xuaunsqfhv7cuuzotagythj4 70 3 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 70 4 Rectangular Rectangular NNP work_53xuaunsqfhv7cuuzotagythj4 70 5 The the DT work_53xuaunsqfhv7cuuzotagythj4 70 6 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 70 7 section section NN work_53xuaunsqfhv7cuuzotagythj4 70 8 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 70 9 or or CC work_53xuaunsqfhv7cuuzotagythj4 70 10 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 70 11 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 70 12 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 70 13 the the DT work_53xuaunsqfhv7cuuzotagythj4 70 14 basis basis NN work_53xuaunsqfhv7cuuzotagythj4 70 15 of of IN work_53xuaunsqfhv7cuuzotagythj4 70 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 70 17 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 70 18 rectangle rectangle NNP work_53xuaunsqfhv7cuuzotagythj4 70 19 , , , work_53xuaunsqfhv7cuuzotagythj4 70 20 whose whose WP$ work_53xuaunsqfhv7cuuzotagythj4 70 21 sides side NNS work_53xuaunsqfhv7cuuzotagythj4 70 22 are be VBP work_53xuaunsqfhv7cuuzotagythj4 70 23 in in IN work_53xuaunsqfhv7cuuzotagythj4 70 24 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 70 25 proportion proportion NN work_53xuaunsqfhv7cuuzotagythj4 70 26 to to IN work_53xuaunsqfhv7cuuzotagythj4 70 27 each each DT work_53xuaunsqfhv7cuuzotagythj4 70 28 other other JJ work_53xuaunsqfhv7cuuzotagythj4 70 29 . . . work_53xuaunsqfhv7cuuzotagythj4 71 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 71 2 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 71 3 rectangle rectangle NN work_53xuaunsqfhv7cuuzotagythj4 71 4 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 71 5 considered consider VBN work_53xuaunsqfhv7cuuzotagythj4 71 6 to to TO work_53xuaunsqfhv7cuuzotagythj4 71 7 be be VB work_53xuaunsqfhv7cuuzotagythj4 71 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 71 9 most most RBS work_53xuaunsqfhv7cuuzotagythj4 71 10 visually visually RB work_53xuaunsqfhv7cuuzotagythj4 71 11 pleasing pleasing JJ work_53xuaunsqfhv7cuuzotagythj4 71 12 of of IN work_53xuaunsqfhv7cuuzotagythj4 71 13 all all DT work_53xuaunsqfhv7cuuzotagythj4 71 14 rectangles rectangle NNS work_53xuaunsqfhv7cuuzotagythj4 71 15 . . . work_53xuaunsqfhv7cuuzotagythj4 72 1 A a DT work_53xuaunsqfhv7cuuzotagythj4 72 2 distinctive distinctive JJ work_53xuaunsqfhv7cuuzotagythj4 72 3 feature feature NN work_53xuaunsqfhv7cuuzotagythj4 72 4 of of IN work_53xuaunsqfhv7cuuzotagythj4 72 5 this this DT work_53xuaunsqfhv7cuuzotagythj4 72 6 shape shape NN work_53xuaunsqfhv7cuuzotagythj4 72 7 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 72 8 that that IN work_53xuaunsqfhv7cuuzotagythj4 72 9 when when WRB work_53xuaunsqfhv7cuuzotagythj4 72 10 a a DT work_53xuaunsqfhv7cuuzotagythj4 72 11 square square JJ work_53xuaunsqfhv7cuuzotagythj4 72 12 section section NN work_53xuaunsqfhv7cuuzotagythj4 72 13 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 72 14 removed remove VBN work_53xuaunsqfhv7cuuzotagythj4 72 15 , , , work_53xuaunsqfhv7cuuzotagythj4 72 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 72 17 remainder remainder NN work_53xuaunsqfhv7cuuzotagythj4 72 18 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 72 19 another another DT work_53xuaunsqfhv7cuuzotagythj4 72 20 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 72 21 rectangle rectangle NN work_53xuaunsqfhv7cuuzotagythj4 72 22 ; ; : work_53xuaunsqfhv7cuuzotagythj4 72 23 that that RB work_53xuaunsqfhv7cuuzotagythj4 72 24 is is RB work_53xuaunsqfhv7cuuzotagythj4 72 25 , , , work_53xuaunsqfhv7cuuzotagythj4 72 26 with with IN work_53xuaunsqfhv7cuuzotagythj4 72 27 the the DT work_53xuaunsqfhv7cuuzotagythj4 72 28 same same JJ work_53xuaunsqfhv7cuuzotagythj4 72 29 aspect aspect NN work_53xuaunsqfhv7cuuzotagythj4 72 30 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 72 31 as as IN work_53xuaunsqfhv7cuuzotagythj4 72 32 the the DT work_53xuaunsqfhv7cuuzotagythj4 72 33 first first JJ work_53xuaunsqfhv7cuuzotagythj4 72 34 . . . work_53xuaunsqfhv7cuuzotagythj4 73 1 Square square JJ work_53xuaunsqfhv7cuuzotagythj4 73 2 removal removal NN work_53xuaunsqfhv7cuuzotagythj4 73 3 can can MD work_53xuaunsqfhv7cuuzotagythj4 73 4 be be VB work_53xuaunsqfhv7cuuzotagythj4 73 5 repeated repeat VBN work_53xuaunsqfhv7cuuzotagythj4 73 6 infinitely infinitely RB work_53xuaunsqfhv7cuuzotagythj4 73 7 , , , work_53xuaunsqfhv7cuuzotagythj4 73 8 in in IN work_53xuaunsqfhv7cuuzotagythj4 73 9 which which WDT work_53xuaunsqfhv7cuuzotagythj4 73 10 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circular circular JJ work_53xuaunsqfhv7cuuzotagythj4 85 7 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 85 8 x x NNP work_53xuaunsqfhv7cuuzotagythj4 85 9 , , , work_53xuaunsqfhv7cuuzotagythj4 85 10 y y NNP work_53xuaunsqfhv7cuuzotagythj4 85 11 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 85 12 pints pint VBZ work_53xuaunsqfhv7cuuzotagythj4 85 13 having have VBG work_53xuaunsqfhv7cuuzotagythj4 85 14 the the DT work_53xuaunsqfhv7cuuzotagythj4 85 15 same same JJ work_53xuaunsqfhv7cuuzotagythj4 85 16 distance distance NN work_53xuaunsqfhv7cuuzotagythj4 85 17 from from IN work_53xuaunsqfhv7cuuzotagythj4 85 18 the the DT work_53xuaunsqfhv7cuuzotagythj4 85 19 center center NN work_53xuaunsqfhv7cuuzotagythj4 85 20 into into IN work_53xuaunsqfhv7cuuzotagythj4 85 21 a a DT work_53xuaunsqfhv7cuuzotagythj4 85 22 spiral spiral JJ work_53xuaunsqfhv7cuuzotagythj4 85 23 form form NN work_53xuaunsqfhv7cuuzotagythj4 85 24 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 85 25 6 6 CD work_53xuaunsqfhv7cuuzotagythj4 85 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rotation NN work_53xuaunsqfhv7cuuzotagythj4 87 6 value value NN work_53xuaunsqfhv7cuuzotagythj4 87 7 each each DT work_53xuaunsqfhv7cuuzotagythj4 87 8 time time NN work_53xuaunsqfhv7cuuzotagythj4 87 9 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 87 10 π(3 π(3 NNP work_53xuaunsqfhv7cuuzotagythj4 87 11 − − NNP work_53xuaunsqfhv7cuuzotagythj4 87 12 √ √ NNP work_53xuaunsqfhv7cuuzotagythj4 87 13 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 87 14 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 87 15 . . . work_53xuaunsqfhv7cuuzotagythj4 88 1 Figure figure NN work_53xuaunsqfhv7cuuzotagythj4 88 2 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 88 3 : : : work_53xuaunsqfhv7cuuzotagythj4 88 4 Simulated simulate VBN work_53xuaunsqfhv7cuuzotagythj4 88 5 spirals spiral NNS work_53xuaunsqfhv7cuuzotagythj4 88 6 in in IN work_53xuaunsqfhv7cuuzotagythj4 88 7 a a DT work_53xuaunsqfhv7cuuzotagythj4 88 8 sunflower sunflower NN work_53xuaunsqfhv7cuuzotagythj4 88 9 with with IN work_53xuaunsqfhv7cuuzotagythj4 88 10 different 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work_53xuaunsqfhv7cuuzotagythj4 89 32 . . . work_53xuaunsqfhv7cuuzotagythj4 90 1 To to TO work_53xuaunsqfhv7cuuzotagythj4 90 2 see see VB work_53xuaunsqfhv7cuuzotagythj4 90 3 the the DT work_53xuaunsqfhv7cuuzotagythj4 90 4 difference difference NN work_53xuaunsqfhv7cuuzotagythj4 90 5 , , , work_53xuaunsqfhv7cuuzotagythj4 90 6 three three CD work_53xuaunsqfhv7cuuzotagythj4 90 7 values value NNS work_53xuaunsqfhv7cuuzotagythj4 90 8 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 90 9 been be VBN work_53xuaunsqfhv7cuuzotagythj4 90 10 used use VBN work_53xuaunsqfhv7cuuzotagythj4 90 11 as as IN work_53xuaunsqfhv7cuuzotagythj4 90 12 rotation rotation NN work_53xuaunsqfhv7cuuzotagythj4 90 13 parameter parameter NN work_53xuaunsqfhv7cuuzotagythj4 90 14 for for IN work_53xuaunsqfhv7cuuzotagythj4 90 15 generating generate VBG work_53xuaunsqfhv7cuuzotagythj4 90 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 90 17 patterns pattern NNS work_53xuaunsqfhv7cuuzotagythj4 90 18 , , , 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A. NNP work_53xuaunsqfhv7cuuzotagythj4 98 22 D. D. 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work_53xuaunsqfhv7cuuzotagythj4 108 26 can can MD work_53xuaunsqfhv7cuuzotagythj4 108 27 produce produce VB work_53xuaunsqfhv7cuuzotagythj4 108 28 truly truly RB work_53xuaunsqfhv7cuuzotagythj4 108 29 random random JJ work_53xuaunsqfhv7cuuzotagythj4 108 30 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 108 31 . . . work_53xuaunsqfhv7cuuzotagythj4 109 1 This this DT work_53xuaunsqfhv7cuuzotagythj4 109 2 explains explain VBZ work_53xuaunsqfhv7cuuzotagythj4 109 3 why why WRB work_53xuaunsqfhv7cuuzotagythj4 109 4 such such JJ work_53xuaunsqfhv7cuuzotagythj4 109 5 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 109 6 are be VBP work_53xuaunsqfhv7cuuzotagythj4 109 7 called call VBN work_53xuaunsqfhv7cuuzotagythj4 109 8 ’ ' '' work_53xuaunsqfhv7cuuzotagythj4 109 9 pseudo pseudo JJ work_53xuaunsqfhv7cuuzotagythj4 109 10 - - JJ work_53xuaunsqfhv7cuuzotagythj4 109 11 random random JJ work_53xuaunsqfhv7cuuzotagythj4 109 12 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 109 13 ’ ' '' work_53xuaunsqfhv7cuuzotagythj4 109 14 . . . work_53xuaunsqfhv7cuuzotagythj4 110 1 Random random JJ work_53xuaunsqfhv7cuuzotagythj4 110 2 number number NN work_53xuaunsqfhv7cuuzotagythj4 110 3 are be VBP work_53xuaunsqfhv7cuuzotagythj4 110 4 used use VBN work_53xuaunsqfhv7cuuzotagythj4 110 5 by by IN work_53xuaunsqfhv7cuuzotagythj4 110 6 many many JJ work_53xuaunsqfhv7cuuzotagythj4 110 7 practical practical JJ work_53xuaunsqfhv7cuuzotagythj4 110 8 applications application NNS work_53xuaunsqfhv7cuuzotagythj4 110 9 including include VBG work_53xuaunsqfhv7cuuzotagythj4 110 10 computer computer NN work_53xuaunsqfhv7cuuzotagythj4 110 11 simulations simulation NNS work_53xuaunsqfhv7cuuzotagythj4 110 12 , , , work_53xuaunsqfhv7cuuzotagythj4 110 13 random random JJ work_53xuaunsqfhv7cuuzotagythj4 110 14 sampling sampling NN work_53xuaunsqfhv7cuuzotagythj4 110 15 , , , work_53xuaunsqfhv7cuuzotagythj4 110 16 numerical numerical JJ work_53xuaunsqfhv7cuuzotagythj4 110 17 analysis analysis NN work_53xuaunsqfhv7cuuzotagythj4 110 18 , , , work_53xuaunsqfhv7cuuzotagythj4 110 19 cryptography cryptography NN work_53xuaunsqfhv7cuuzotagythj4 110 20 and and CC work_53xuaunsqfhv7cuuzotagythj4 110 21 communications communication NNS work_53xuaunsqfhv7cuuzotagythj4 110 22 industry industry NN work_53xuaunsqfhv7cuuzotagythj4 110 23 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 110 24 15 15 CD work_53xuaunsqfhv7cuuzotagythj4 110 25 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 110 26 . . . work_53xuaunsqfhv7cuuzotagythj4 111 1 Different different JJ work_53xuaunsqfhv7cuuzotagythj4 111 2 statistical statistical JJ work_53xuaunsqfhv7cuuzotagythj4 111 3 test test NN work_53xuaunsqfhv7cuuzotagythj4 111 4 are be VBP work_53xuaunsqfhv7cuuzotagythj4 111 5 designed design VBN work_53xuaunsqfhv7cuuzotagythj4 111 6 to to TO work_53xuaunsqfhv7cuuzotagythj4 111 7 test test VB work_53xuaunsqfhv7cuuzotagythj4 111 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 111 9 null null NN work_53xuaunsqfhv7cuuzotagythj4 111 10 hypothesis hypothesis NN work_53xuaunsqfhv7cuuzotagythj4 111 11 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 111 12 H0 H0 NNP work_53xuaunsqfhv7cuuzotagythj4 111 13 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 111 14 which which WDT work_53xuaunsqfhv7cuuzotagythj4 111 15 states state VBZ work_53xuaunsqfhv7cuuzotagythj4 111 16 a a DT work_53xuaunsqfhv7cuuzotagythj4 111 17 given give VBN work_53xuaunsqfhv7cuuzotagythj4 111 18 pseudo pseudo NN work_53xuaunsqfhv7cuuzotagythj4 111 19 - - JJ work_53xuaunsqfhv7cuuzotagythj4 111 20 random random JJ work_53xuaunsqfhv7cuuzotagythj4 111 21 number number NN work_53xuaunsqfhv7cuuzotagythj4 111 22 generator generator NN work_53xuaunsqfhv7cuuzotagythj4 111 23 produces produce VBZ work_53xuaunsqfhv7cuuzotagythj4 111 24 ’ ' '' work_53xuaunsqfhv7cuuzotagythj4 111 25 sufficiently sufficiently RB work_53xuaunsqfhv7cuuzotagythj4 111 26 ’ ' '' work_53xuaunsqfhv7cuuzotagythj4 111 27 random random JJ work_53xuaunsqfhv7cuuzotagythj4 111 28 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 111 29 of of IN work_53xuaunsqfhv7cuuzotagythj4 111 30 numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 111 31 for for IN work_53xuaunsqfhv7cuuzotagythj4 111 32 their -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 111 33 intended intend VBN work_53xuaunsqfhv7cuuzotagythj4 111 34 use use NN work_53xuaunsqfhv7cuuzotagythj4 111 35 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 111 36 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 111 37 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 111 38 . . . work_53xuaunsqfhv7cuuzotagythj4 112 1 These these DT work_53xuaunsqfhv7cuuzotagythj4 112 2 randomness randomness NN work_53xuaunsqfhv7cuuzotagythj4 112 3 tests test NNS work_53xuaunsqfhv7cuuzotagythj4 112 4 are be VBP work_53xuaunsqfhv7cuuzotagythj4 112 5 proba- proba- FW work_53xuaunsqfhv7cuuzotagythj4 112 6 bilistic bilistic JJ work_53xuaunsqfhv7cuuzotagythj4 112 7 and and CC work_53xuaunsqfhv7cuuzotagythj4 112 8 involve involve VB work_53xuaunsqfhv7cuuzotagythj4 112 9 two two CD 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be VBZ work_53xuaunsqfhv7cuuzotagythj4 113 17 occurred occur VBN work_53xuaunsqfhv7cuuzotagythj4 113 18 and and CC work_53xuaunsqfhv7cuuzotagythj4 113 19 if if IN work_53xuaunsqfhv7cuuzotagythj4 113 20 the the DT work_53xuaunsqfhv7cuuzotagythj4 113 21 data datum NNS work_53xuaunsqfhv7cuuzotagythj4 113 22 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 113 23 non non JJ work_53xuaunsqfhv7cuuzotagythj4 113 24 - - JJ work_53xuaunsqfhv7cuuzotagythj4 113 25 random random JJ work_53xuaunsqfhv7cuuzotagythj4 113 26 and and CC work_53xuaunsqfhv7cuuzotagythj4 113 27 H0 h0 NN work_53xuaunsqfhv7cuuzotagythj4 113 28 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 113 29 accepted accept VBN work_53xuaunsqfhv7cuuzotagythj4 113 30 , , , work_53xuaunsqfhv7cuuzotagythj4 113 31 type type NN work_53xuaunsqfhv7cuuzotagythj4 113 32 II II NNP work_53xuaunsqfhv7cuuzotagythj4 113 33 error error NN work_53xuaunsqfhv7cuuzotagythj4 113 34 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 113 35 occurred occur VBN work_53xuaunsqfhv7cuuzotagythj4 113 36 . . . work_53xuaunsqfhv7cuuzotagythj4 114 1 In in IN work_53xuaunsqfhv7cuuzotagythj4 114 2 the the DT work_53xuaunsqfhv7cuuzotagythj4 114 3 following following NN work_53xuaunsqfhv7cuuzotagythj4 114 4 , , , work_53xuaunsqfhv7cuuzotagythj4 114 5 the the DT work_53xuaunsqfhv7cuuzotagythj4 114 6 first first JJ work_53xuaunsqfhv7cuuzotagythj4 114 7 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 114 8 of of IN work_53xuaunsqfhv7cuuzotagythj4 114 9 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 114 10 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 114 11 of of IN work_53xuaunsqfhv7cuuzotagythj4 114 12 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 114 13 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 114 14 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 114 15 been be VBN work_53xuaunsqfhv7cuuzotagythj4 114 16 ex- ex- VBN work_53xuaunsqfhv7cuuzotagythj4 114 17 amined amine VBN work_53xuaunsqfhv7cuuzotagythj4 114 18 to to TO work_53xuaunsqfhv7cuuzotagythj4 114 19 answer answer VB work_53xuaunsqfhv7cuuzotagythj4 114 20 the the DT work_53xuaunsqfhv7cuuzotagythj4 114 21 question question NN work_53xuaunsqfhv7cuuzotagythj4 114 22 of of IN work_53xuaunsqfhv7cuuzotagythj4 114 23 whether whether IN work_53xuaunsqfhv7cuuzotagythj4 114 24 these these DT work_53xuaunsqfhv7cuuzotagythj4 114 25 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 114 26 form form VBP work_53xuaunsqfhv7cuuzotagythj4 114 27 a a DT work_53xuaunsqfhv7cuuzotagythj4 114 28 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 114 29 of of IN work_53xuaunsqfhv7cuuzotagythj4 114 30 random random JJ work_53xuaunsqfhv7cuuzotagythj4 114 31 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 114 32 . . . work_53xuaunsqfhv7cuuzotagythj4 115 1 These these DT work_53xuaunsqfhv7cuuzotagythj4 115 2 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 115 3 were be VBD work_53xuaunsqfhv7cuuzotagythj4 115 4 obtained obtain VBN work_53xuaunsqfhv7cuuzotagythj4 115 5 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to TO work_53xuaunsqfhv7cuuzotagythj4 115 25 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 115 26 million million CD work_53xuaunsqfhv7cuuzotagythj4 115 27 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 115 28 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 115 29 , , , work_53xuaunsqfhv7cuuzotagythj4 115 30 devel- devel- NNP work_53xuaunsqfhv7cuuzotagythj4 115 31 oped ope VBN work_53xuaunsqfhv7cuuzotagythj4 115 32 by by IN work_53xuaunsqfhv7cuuzotagythj4 115 33 Alireza Alireza NNP work_53xuaunsqfhv7cuuzotagythj4 115 34 Shafaei Shafaei NNP work_53xuaunsqfhv7cuuzotagythj4 115 35 , , , work_53xuaunsqfhv7cuuzotagythj4 115 36 which which WDT work_53xuaunsqfhv7cuuzotagythj4 115 37 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 115 38 available available JJ work_53xuaunsqfhv7cuuzotagythj4 115 39 for for IN work_53xuaunsqfhv7cuuzotagythj4 115 40 download download NN work_53xuaunsqfhv7cuuzotagythj4 115 41 through through IN work_53xuaunsqfhv7cuuzotagythj4 115 42 https://alireza- https://alireza- . work_53xuaunsqfhv7cuuzotagythj4 115 43 shafaei.software.informer.com shafaei.software.informer.com NNP work_53xuaunsqfhv7cuuzotagythj4 115 44 . . . work_53xuaunsqfhv7cuuzotagythj4 116 1 First first RB work_53xuaunsqfhv7cuuzotagythj4 116 2 of of IN work_53xuaunsqfhv7cuuzotagythj4 116 3 all all DT work_53xuaunsqfhv7cuuzotagythj4 116 4 , , , work_53xuaunsqfhv7cuuzotagythj4 116 5 Table table NN work_53xuaunsqfhv7cuuzotagythj4 116 6 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 116 7 shows show VBZ work_53xuaunsqfhv7cuuzotagythj4 116 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 116 9 frequency frequency NN work_53xuaunsqfhv7cuuzotagythj4 116 10 of of IN work_53xuaunsqfhv7cuuzotagythj4 116 11 the the DT work_53xuaunsqfhv7cuuzotagythj4 116 12 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 116 13 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 116 14 through through IN work_53xuaunsqfhv7cuuzotagythj4 116 15 9 9 CD work_53xuaunsqfhv7cuuzotagythj4 116 16 for for IN work_53xuaunsqfhv7cuuzotagythj4 116 17 the the DT work_53xuaunsqfhv7cuuzotagythj4 116 18 first first JJ work_53xuaunsqfhv7cuuzotagythj4 116 19 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 116 20 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 116 21 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 116 22 of of IN work_53xuaunsqfhv7cuuzotagythj4 116 23 the the DT work_53xuaunsqfhv7cuuzotagythj4 116 24 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 116 25 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 116 26 , , , work_53xuaunsqfhv7cuuzotagythj4 116 27 confirming confirm VBG work_53xuaunsqfhv7cuuzotagythj4 116 28 these these DT work_53xuaunsqfhv7cuuzotagythj4 116 29 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 116 30 are be VBP work_53xuaunsqfhv7cuuzotagythj4 116 31 uniformly uniformly RB work_53xuaunsqfhv7cuuzotagythj4 116 32 distributed distribute VBN work_53xuaunsqfhv7cuuzotagythj4 116 33 . . . work_53xuaunsqfhv7cuuzotagythj4 117 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 117 2 result result NN work_53xuaunsqfhv7cuuzotagythj4 117 3 of of IN work_53xuaunsqfhv7cuuzotagythj4 117 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 117 5 chi chi JJ work_53xuaunsqfhv7cuuzotagythj4 117 6 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 117 7 square square JJ work_53xuaunsqfhv7cuuzotagythj4 117 8 test test NN work_53xuaunsqfhv7cuuzotagythj4 117 9 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 117 10 χ2=1.3112 χ2=1.3112 NNP work_53xuaunsqfhv7cuuzotagythj4 117 11 , , , work_53xuaunsqfhv7cuuzotagythj4 117 12 df=9 df=9 XX work_53xuaunsqfhv7cuuzotagythj4 117 13 , , , work_53xuaunsqfhv7cuuzotagythj4 117 14 p p NN work_53xuaunsqfhv7cuuzotagythj4 117 15 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 117 16 value= value= NN work_53xuaunsqfhv7cuuzotagythj4 117 17 0.9983 0.9983 CD work_53xuaunsqfhv7cuuzotagythj4 117 18 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 117 19 applied apply VBD work_53xuaunsqfhv7cuuzotagythj4 117 20 on on IN work_53xuaunsqfhv7cuuzotagythj4 117 21 the the DT work_53xuaunsqfhv7cuuzotagythj4 117 22 counts count NNS work_53xuaunsqfhv7cuuzotagythj4 117 23 obtained obtain VBN work_53xuaunsqfhv7cuuzotagythj4 117 24 in in IN work_53xuaunsqfhv7cuuzotagythj4 117 25 Table table NN work_53xuaunsqfhv7cuuzotagythj4 117 26 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 117 27 do do VBP work_53xuaunsqfhv7cuuzotagythj4 117 28 not not RB work_53xuaunsqfhv7cuuzotagythj4 117 29 reject reject VB work_53xuaunsqfhv7cuuzotagythj4 117 30 the the DT work_53xuaunsqfhv7cuuzotagythj4 117 31 null null JJ work_53xuaunsqfhv7cuuzotagythj4 117 32 hypothesis hypothesis NN work_53xuaunsqfhv7cuuzotagythj4 117 33 that that IN work_53xuaunsqfhv7cuuzotagythj4 117 34 each each DT work_53xuaunsqfhv7cuuzotagythj4 117 35 of of IN work_53xuaunsqfhv7cuuzotagythj4 117 36 the the DT work_53xuaunsqfhv7cuuzotagythj4 117 37 ten ten NN work_53xuaunsqfhv7cuuzotagythj4 117 38 digits digit VBZ work_53xuaunsqfhv7cuuzotagythj4 117 39 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 117 40 through through IN work_53xuaunsqfhv7cuuzotagythj4 117 41 9 9 CD work_53xuaunsqfhv7cuuzotagythj4 117 42 has have VBZ work_53xuaunsqfhv7cuuzotagythj4 117 43 been be VBN work_53xuaunsqfhv7cuuzotagythj4 117 44 occurred occur VBN work_53xuaunsqfhv7cuuzotagythj4 117 45 with with IN work_53xuaunsqfhv7cuuzotagythj4 117 46 probability probability NN work_53xuaunsqfhv7cuuzotagythj4 117 47 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 117 48 10 10 CD work_53xuaunsqfhv7cuuzotagythj4 117 49 . . . work_53xuaunsqfhv7cuuzotagythj4 118 1 Then then RB work_53xuaunsqfhv7cuuzotagythj4 118 2 the the DT work_53xuaunsqfhv7cuuzotagythj4 118 3 Durbin Durbin NNP work_53xuaunsqfhv7cuuzotagythj4 118 4 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 118 5 Watson Watson NNP work_53xuaunsqfhv7cuuzotagythj4 118 6 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 118 7 DW DW NNP work_53xuaunsqfhv7cuuzotagythj4 118 8 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 118 9 test test NN work_53xuaunsqfhv7cuuzotagythj4 118 10 , , , work_53xuaunsqfhv7cuuzotagythj4 118 11 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 118 12 used use VBN work_53xuaunsqfhv7cuuzotagythj4 118 13 for for IN work_53xuaunsqfhv7cuuzotagythj4 118 14 testing test VBG work_53xuaunsqfhv7cuuzotagythj4 118 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 118 16 null null NN work_53xuaunsqfhv7cuuzotagythj4 118 17 hypothesis hypothesis NN work_53xuaunsqfhv7cuuzotagythj4 118 18 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 118 19 Hamid Hamid NNP work_53xuaunsqfhv7cuuzotagythj4 118 20 Ghorbani Ghorbani NNP work_53xuaunsqfhv7cuuzotagythj4 118 21 Table table NN work_53xuaunsqfhv7cuuzotagythj4 118 22 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 118 23 : : : work_53xuaunsqfhv7cuuzotagythj4 118 24 Counts count NNS work_53xuaunsqfhv7cuuzotagythj4 118 25 of of IN work_53xuaunsqfhv7cuuzotagythj4 118 26 the the DT work_53xuaunsqfhv7cuuzotagythj4 118 27 first first JJ work_53xuaunsqfhv7cuuzotagythj4 118 28 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 118 29 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 118 30 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 118 31 of of IN work_53xuaunsqfhv7cuuzotagythj4 118 32 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 118 33 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 118 34 . . . work_53xuaunsqfhv7cuuzotagythj4 119 1 digits digits NNP work_53xuaunsqfhv7cuuzotagythj4 119 2 0 0 CD work_53xuaunsqfhv7cuuzotagythj4 119 3 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 119 4 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 119 5 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 119 6 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 119 7 frequenct frequenct JJ work_53xuaunsqfhv7cuuzotagythj4 119 8 9986 9986 CD work_53xuaunsqfhv7cuuzotagythj4 119 9 9963 9963 CD work_53xuaunsqfhv7cuuzotagythj4 119 10 9950 9950 CD work_53xuaunsqfhv7cuuzotagythj4 119 11 10079 10079 CD work_53xuaunsqfhv7cuuzotagythj4 119 12 10041 10041 CD work_53xuaunsqfhv7cuuzotagythj4 119 13 digits digit VBZ work_53xuaunsqfhv7cuuzotagythj4 119 14 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 119 15 6 6 CD work_53xuaunsqfhv7cuuzotagythj4 119 16 7 7 CD work_53xuaunsqfhv7cuuzotagythj4 119 17 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 119 18 9 9 CD work_53xuaunsqfhv7cuuzotagythj4 119 19 frequenct frequenct JJ work_53xuaunsqfhv7cuuzotagythj4 119 20 10016 10016 CD work_53xuaunsqfhv7cuuzotagythj4 119 21 9975 9975 CD work_53xuaunsqfhv7cuuzotagythj4 119 22 9988 9988 CD work_53xuaunsqfhv7cuuzotagythj4 119 23 1008 1008 CD work_53xuaunsqfhv7cuuzotagythj4 119 24 9994 9994 CD work_53xuaunsqfhv7cuuzotagythj4 119 25 claiming claim VBG work_53xuaunsqfhv7cuuzotagythj4 119 26 the the DT work_53xuaunsqfhv7cuuzotagythj4 119 27 specific specific JJ work_53xuaunsqfhv7cuuzotagythj4 119 28 lag lag NNP work_53xuaunsqfhv7cuuzotagythj4 119 29 k k NNP work_53xuaunsqfhv7cuuzotagythj4 119 30 autocorrelation autocorrelation NN work_53xuaunsqfhv7cuuzotagythj4 119 31 in in IN work_53xuaunsqfhv7cuuzotagythj4 119 32 the the DT work_53xuaunsqfhv7cuuzotagythj4 119 33 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 119 34 of of IN work_53xuaunsqfhv7cuuzotagythj4 119 35 the the DT work_53xuaunsqfhv7cuuzotagythj4 119 36 first first JJ work_53xuaunsqfhv7cuuzotagythj4 119 37 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 119 38 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 119 39 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 119 40 of of IN work_53xuaunsqfhv7cuuzotagythj4 119 41 the the DT work_53xuaunsqfhv7cuuzotagythj4 119 42 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 119 43 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 119 44 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 119 45 zero zero CD work_53xuaunsqfhv7cuuzotagythj4 119 46 . . . work_53xuaunsqfhv7cuuzotagythj4 120 1 Table table NN work_53xuaunsqfhv7cuuzotagythj4 120 2 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 120 3 shows show VBZ work_53xuaunsqfhv7cuuzotagythj4 120 4 the the DT work_53xuaunsqfhv7cuuzotagythj4 120 5 results result NNS work_53xuaunsqfhv7cuuzotagythj4 120 6 of of IN work_53xuaunsqfhv7cuuzotagythj4 120 7 conducting conduct VBG work_53xuaunsqfhv7cuuzotagythj4 120 8 the the DT work_53xuaunsqfhv7cuuzotagythj4 120 9 Durbin Durbin NNP work_53xuaunsqfhv7cuuzotagythj4 120 10 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 120 11 Watson Watson NNP work_53xuaunsqfhv7cuuzotagythj4 120 12 test test NN work_53xuaunsqfhv7cuuzotagythj4 120 13 for for IN work_53xuaunsqfhv7cuuzotagythj4 120 14 the the DT work_53xuaunsqfhv7cuuzotagythj4 120 15 first first JJ work_53xuaunsqfhv7cuuzotagythj4 120 16 through through IN work_53xuaunsqfhv7cuuzotagythj4 120 17 fifth fifth JJ work_53xuaunsqfhv7cuuzotagythj4 120 18 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 120 19 order order NN work_53xuaunsqfhv7cuuzotagythj4 120 20 autocorrelation autocorrelation NN work_53xuaunsqfhv7cuuzotagythj4 120 21 of of IN work_53xuaunsqfhv7cuuzotagythj4 120 22 this this DT work_53xuaunsqfhv7cuuzotagythj4 120 23 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 120 24 , , , work_53xuaunsqfhv7cuuzotagythj4 120 25 which which WDT work_53xuaunsqfhv7cuuzotagythj4 120 26 shows show VBZ work_53xuaunsqfhv7cuuzotagythj4 120 27 no no DT work_53xuaunsqfhv7cuuzotagythj4 120 28 significant significant JJ work_53xuaunsqfhv7cuuzotagythj4 120 29 autocorrelation autocorrelation NN work_53xuaunsqfhv7cuuzotagythj4 120 30 through through IN work_53xuaunsqfhv7cuuzotagythj4 120 31 fifth fifth JJ work_53xuaunsqfhv7cuuzotagythj4 120 32 order order NN work_53xuaunsqfhv7cuuzotagythj4 120 33 . . . work_53xuaunsqfhv7cuuzotagythj4 121 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 121 2 same same JJ work_53xuaunsqfhv7cuuzotagythj4 121 3 results result NNS work_53xuaunsqfhv7cuuzotagythj4 121 4 are be VBP work_53xuaunsqfhv7cuuzotagythj4 121 5 obtained obtain VBN work_53xuaunsqfhv7cuuzotagythj4 121 6 for for IN work_53xuaunsqfhv7cuuzotagythj4 121 7 higher high JJR work_53xuaunsqfhv7cuuzotagythj4 121 8 orders order NNS work_53xuaunsqfhv7cuuzotagythj4 121 9 of of IN work_53xuaunsqfhv7cuuzotagythj4 121 10 k. k. NNP work_53xuaunsqfhv7cuuzotagythj4 121 11 Therefore therefore RB work_53xuaunsqfhv7cuuzotagythj4 121 12 , , , work_53xuaunsqfhv7cuuzotagythj4 121 13 according accord VBG work_53xuaunsqfhv7cuuzotagythj4 121 14 to to IN work_53xuaunsqfhv7cuuzotagythj4 121 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 121 16 results result NNS work_53xuaunsqfhv7cuuzotagythj4 121 17 of of IN work_53xuaunsqfhv7cuuzotagythj4 121 18 both both DT work_53xuaunsqfhv7cuuzotagythj4 121 19 chi chi JJ work_53xuaunsqfhv7cuuzotagythj4 121 20 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 121 21 square square NNP work_53xuaunsqfhv7cuuzotagythj4 121 22 and and CC work_53xuaunsqfhv7cuuzotagythj4 121 23 DW DW NNP work_53xuaunsqfhv7cuuzotagythj4 121 24 tests test VBZ work_53xuaunsqfhv7cuuzotagythj4 121 25 the the DT work_53xuaunsqfhv7cuuzotagythj4 121 26 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 121 27 of of IN work_53xuaunsqfhv7cuuzotagythj4 121 28 the the DT work_53xuaunsqfhv7cuuzotagythj4 121 29 first first JJ work_53xuaunsqfhv7cuuzotagythj4 121 30 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 121 31 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 121 32 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 121 33 of of IN work_53xuaunsqfhv7cuuzotagythj4 121 34 the the DT work_53xuaunsqfhv7cuuzotagythj4 121 35 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 121 36 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 121 37 are be VBP work_53xuaunsqfhv7cuuzotagythj4 121 38 indistinguishable indistinguishable JJ work_53xuaunsqfhv7cuuzotagythj4 121 39 from from IN work_53xuaunsqfhv7cuuzotagythj4 121 40 a a DT work_53xuaunsqfhv7cuuzotagythj4 121 41 random random JJ work_53xuaunsqfhv7cuuzotagythj4 121 42 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 121 43 . . . work_53xuaunsqfhv7cuuzotagythj4 122 1 Table table NN work_53xuaunsqfhv7cuuzotagythj4 122 2 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 122 3 : : : work_53xuaunsqfhv7cuuzotagythj4 122 4 Durbin Durbin NNP work_53xuaunsqfhv7cuuzotagythj4 122 5 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 122 6 Watson Watson NNP work_53xuaunsqfhv7cuuzotagythj4 122 7 test test NN work_53xuaunsqfhv7cuuzotagythj4 122 8 applied apply VBD work_53xuaunsqfhv7cuuzotagythj4 122 9 on on IN work_53xuaunsqfhv7cuuzotagythj4 122 10 the the DT work_53xuaunsqfhv7cuuzotagythj4 122 11 first first JJ work_53xuaunsqfhv7cuuzotagythj4 122 12 100,000 100,000 CD work_53xuaunsqfhv7cuuzotagythj4 122 13 decimal decimal JJ work_53xuaunsqfhv7cuuzotagythj4 122 14 digits digit NNS work_53xuaunsqfhv7cuuzotagythj4 122 15 of of IN work_53xuaunsqfhv7cuuzotagythj4 122 16 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 122 17 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 122 18 . . . work_53xuaunsqfhv7cuuzotagythj4 123 1 lag lag NNP work_53xuaunsqfhv7cuuzotagythj4 123 2 Autocorrelation Autocorrelation NNP work_53xuaunsqfhv7cuuzotagythj4 123 3 D D NNP work_53xuaunsqfhv7cuuzotagythj4 123 4 - - : work_53xuaunsqfhv7cuuzotagythj4 123 5 W W NNP work_53xuaunsqfhv7cuuzotagythj4 123 6 Statistic Statistic NNP work_53xuaunsqfhv7cuuzotagythj4 123 7 p p NN work_53xuaunsqfhv7cuuzotagythj4 123 8 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 123 9 value value NN work_53xuaunsqfhv7cuuzotagythj4 123 10 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 123 11 +0.002 +0.002 $ work_53xuaunsqfhv7cuuzotagythj4 123 12 1.996 1.996 CD work_53xuaunsqfhv7cuuzotagythj4 123 13 0.476 0.476 CD work_53xuaunsqfhv7cuuzotagythj4 123 14 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 123 15 −0.002 −0.002 CD work_53xuaunsqfhv7cuuzotagythj4 123 16 2.003 2.003 CD work_53xuaunsqfhv7cuuzotagythj4 123 17 0.578 0.578 CD work_53xuaunsqfhv7cuuzotagythj4 123 18 3 3 CD work_53xuaunsqfhv7cuuzotagythj4 123 19 +0.001 +0.001 NN work_53xuaunsqfhv7cuuzotagythj4 123 20 1.999 1.999 CD work_53xuaunsqfhv7cuuzotagythj4 123 21 0.692 0.692 CD work_53xuaunsqfhv7cuuzotagythj4 123 22 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 123 23 +0.002 +0.002 $ work_53xuaunsqfhv7cuuzotagythj4 123 24 1.995 1.995 CD work_53xuaunsqfhv7cuuzotagythj4 123 25 0.408 0.408 CD work_53xuaunsqfhv7cuuzotagythj4 123 26 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 123 27 −0.000 −0.000 NNS work_53xuaunsqfhv7cuuzotagythj4 123 28 2.000 2.000 CD work_53xuaunsqfhv7cuuzotagythj4 123 29 0.776 0.776 CD work_53xuaunsqfhv7cuuzotagythj4 123 30 Conflicts conflict NNS work_53xuaunsqfhv7cuuzotagythj4 123 31 of of IN work_53xuaunsqfhv7cuuzotagythj4 123 32 Interest Interest NNP work_53xuaunsqfhv7cuuzotagythj4 123 33 . . . work_53xuaunsqfhv7cuuzotagythj4 124 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 124 2 author author NN work_53xuaunsqfhv7cuuzotagythj4 124 3 declares declare VBZ work_53xuaunsqfhv7cuuzotagythj4 124 4 that that IN work_53xuaunsqfhv7cuuzotagythj4 124 5 there there EX work_53xuaunsqfhv7cuuzotagythj4 124 6 is be VBZ work_53xuaunsqfhv7cuuzotagythj4 124 7 no no DT work_53xuaunsqfhv7cuuzotagythj4 124 8 conflicts conflict NNS work_53xuaunsqfhv7cuuzotagythj4 124 9 of of IN work_53xuaunsqfhv7cuuzotagythj4 124 10 interest interest NN work_53xuaunsqfhv7cuuzotagythj4 124 11 regarding regard VBG work_53xuaunsqfhv7cuuzotagythj4 124 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 124 13 publication publication NN work_53xuaunsqfhv7cuuzotagythj4 124 14 of of IN work_53xuaunsqfhv7cuuzotagythj4 124 15 this this DT work_53xuaunsqfhv7cuuzotagythj4 124 16 article article NN work_53xuaunsqfhv7cuuzotagythj4 124 17 . . . work_53xuaunsqfhv7cuuzotagythj4 125 1 References reference NNS work_53xuaunsqfhv7cuuzotagythj4 125 2 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 125 3 1 1 CD work_53xuaunsqfhv7cuuzotagythj4 125 4 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 125 5 D. D. NNP work_53xuaunsqfhv7cuuzotagythj4 125 6 Biebighauser Biebighauser NNP work_53xuaunsqfhv7cuuzotagythj4 125 7 , , , work_53xuaunsqfhv7cuuzotagythj4 125 8 Testing test VBG work_53xuaunsqfhv7cuuzotagythj4 125 9 random random JJ work_53xuaunsqfhv7cuuzotagythj4 125 10 number number NN work_53xuaunsqfhv7cuuzotagythj4 125 11 generators generator NNS work_53xuaunsqfhv7cuuzotagythj4 125 12 , , , work_53xuaunsqfhv7cuuzotagythj4 125 13 unpublished unpublished JJ work_53xuaunsqfhv7cuuzotagythj4 125 14 research research NN work_53xuaunsqfhv7cuuzotagythj4 125 15 paper paper NN work_53xuaunsqfhv7cuuzotagythj4 125 16 , , , work_53xuaunsqfhv7cuuzotagythj4 125 17 University University NNP work_53xuaunsqfhv7cuuzotagythj4 125 18 of of IN work_53xuaunsqfhv7cuuzotagythj4 125 19 Minnesota Minnesota NNP work_53xuaunsqfhv7cuuzotagythj4 125 20 , , , work_53xuaunsqfhv7cuuzotagythj4 125 21 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 125 22 2000 2000 CD work_53xuaunsqfhv7cuuzotagythj4 125 23 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 125 24 . . . work_53xuaunsqfhv7cuuzotagythj4 126 1 Url Url NNP work_53xuaunsqfhv7cuuzotagythj4 126 2 = = SYM work_53xuaunsqfhv7cuuzotagythj4 126 3 " " `` work_53xuaunsqfhv7cuuzotagythj4 126 4 www- www- RB work_53xuaunsqfhv7cuuzotagythj4 126 5 users.math.umn.edu/ users.math.umn.edu/ NNP work_53xuaunsqfhv7cuuzotagythj4 126 6 garrett garrett NNP work_53xuaunsqfhv7cuuzotagythj4 126 7 / / SYM work_53xuaunsqfhv7cuuzotagythj4 126 8 students student NNS work_53xuaunsqfhv7cuuzotagythj4 126 9 / / SYM work_53xuaunsqfhv7cuuzotagythj4 126 10 reu reu NNP work_53xuaunsqfhv7cuuzotagythj4 126 11 / / SYM work_53xuaunsqfhv7cuuzotagythj4 126 12 pRNGs.pdf pRNGs.pdf NNP work_53xuaunsqfhv7cuuzotagythj4 126 13 " " '' work_53xuaunsqfhv7cuuzotagythj4 126 14 . . . work_53xuaunsqfhv7cuuzotagythj4 127 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 127 2 2 2 LS work_53xuaunsqfhv7cuuzotagythj4 127 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 127 4 L. L. NNP work_53xuaunsqfhv7cuuzotagythj4 127 5 Corbusier Corbusier NNP work_53xuaunsqfhv7cuuzotagythj4 127 6 , , , work_53xuaunsqfhv7cuuzotagythj4 127 7 Modulor Modulor NNP work_53xuaunsqfhv7cuuzotagythj4 127 8 I I NNP work_53xuaunsqfhv7cuuzotagythj4 127 9 and and CC work_53xuaunsqfhv7cuuzotagythj4 127 10 II II NNP work_53xuaunsqfhv7cuuzotagythj4 127 11 , , , work_53xuaunsqfhv7cuuzotagythj4 127 12 Translated translate VBN work_53xuaunsqfhv7cuuzotagythj4 127 13 by by IN work_53xuaunsqfhv7cuuzotagythj4 127 14 P. P. NNP work_53xuaunsqfhv7cuuzotagythj4 127 15 de de FW work_53xuaunsqfhv7cuuzotagythj4 127 16 Francia Francia NNP work_53xuaunsqfhv7cuuzotagythj4 127 17 and and CC work_53xuaunsqfhv7cuuzotagythj4 127 18 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 127 19 A. a. NN work_53xuaunsqfhv7cuuzotagythj4 127 20 Bostock Bostock NNP work_53xuaunsqfhv7cuuzotagythj4 127 21 , , , work_53xuaunsqfhv7cuuzotagythj4 127 22 Harvard Harvard NNP work_53xuaunsqfhv7cuuzotagythj4 127 23 University University NNP work_53xuaunsqfhv7cuuzotagythj4 127 24 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 127 25 , , , work_53xuaunsqfhv7cuuzotagythj4 127 26 Cambridge Cambridge NNP work_53xuaunsqfhv7cuuzotagythj4 127 27 , , , work_53xuaunsqfhv7cuuzotagythj4 127 28 1980 1980 CD work_53xuaunsqfhv7cuuzotagythj4 127 29 . . . work_53xuaunsqfhv7cuuzotagythj4 128 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 128 2 3 3 LS work_53xuaunsqfhv7cuuzotagythj4 128 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 128 4 L. L. NNP work_53xuaunsqfhv7cuuzotagythj4 128 5 M. M. NNP work_53xuaunsqfhv7cuuzotagythj4 128 6 Dabbour Dabbour NNP work_53xuaunsqfhv7cuuzotagythj4 128 7 , , , work_53xuaunsqfhv7cuuzotagythj4 128 8 Geometric geometric JJ work_53xuaunsqfhv7cuuzotagythj4 128 9 proportions proportion NNS work_53xuaunsqfhv7cuuzotagythj4 128 10 , , , work_53xuaunsqfhv7cuuzotagythj4 128 11 The the DT work_53xuaunsqfhv7cuuzotagythj4 128 12 underlying underlie VBG work_53xuaunsqfhv7cuuzotagythj4 128 13 structure structure NN work_53xuaunsqfhv7cuuzotagythj4 128 14 of of IN work_53xuaunsqfhv7cuuzotagythj4 128 15 design design NN work_53xuaunsqfhv7cuuzotagythj4 128 16 process process NN work_53xuaunsqfhv7cuuzotagythj4 128 17 for for IN work_53xuaunsqfhv7cuuzotagythj4 128 18 Islamic islamic JJ work_53xuaunsqfhv7cuuzotagythj4 128 19 geometric geometric JJ work_53xuaunsqfhv7cuuzotagythj4 128 20 patterns pattern NNS work_53xuaunsqfhv7cuuzotagythj4 128 21 , , , work_53xuaunsqfhv7cuuzotagythj4 128 22 Front front NN work_53xuaunsqfhv7cuuzotagythj4 128 23 . . . work_53xuaunsqfhv7cuuzotagythj4 129 1 Archit archit VB work_53xuaunsqfhv7cuuzotagythj4 129 2 . . . work_53xuaunsqfhv7cuuzotagythj4 130 1 Res Res NNP work_53xuaunsqfhv7cuuzotagythj4 130 2 . . . work_53xuaunsqfhv7cuuzotagythj4 131 1 1(4 1(4 NNP work_53xuaunsqfhv7cuuzotagythj4 131 2 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 131 3 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 131 4 2012 2012 CD work_53xuaunsqfhv7cuuzotagythj4 131 5 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 131 6 380 380 CD work_53xuaunsqfhv7cuuzotagythj4 131 7 − − NNP work_53xuaunsqfhv7cuuzotagythj4 131 8 391 391 CD work_53xuaunsqfhv7cuuzotagythj4 131 9 . . . work_53xuaunsqfhv7cuuzotagythj4 132 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 132 2 4 4 CD work_53xuaunsqfhv7cuuzotagythj4 132 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 132 4 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 132 5 A. A. NNP work_53xuaunsqfhv7cuuzotagythj4 132 6 Dunlap Dunlap NNP work_53xuaunsqfhv7cuuzotagythj4 132 7 , , , work_53xuaunsqfhv7cuuzotagythj4 132 8 The the DT work_53xuaunsqfhv7cuuzotagythj4 132 9 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 132 10 Ratio Ratio NNP work_53xuaunsqfhv7cuuzotagythj4 132 11 and and CC work_53xuaunsqfhv7cuuzotagythj4 132 12 Fibonacci Fibonacci NNP work_53xuaunsqfhv7cuuzotagythj4 132 13 Numbers Numbers NNPS work_53xuaunsqfhv7cuuzotagythj4 132 14 , , , work_53xuaunsqfhv7cuuzotagythj4 132 15 World World NNP work_53xuaunsqfhv7cuuzotagythj4 132 16 Scientific Scientific NNP work_53xuaunsqfhv7cuuzotagythj4 132 17 Publishing Publishing NNP work_53xuaunsqfhv7cuuzotagythj4 132 18 Co. Co. NNP work_53xuaunsqfhv7cuuzotagythj4 132 19 , , , work_53xuaunsqfhv7cuuzotagythj4 132 20 New New NNP work_53xuaunsqfhv7cuuzotagythj4 132 21 Jersey Jersey NNP work_53xuaunsqfhv7cuuzotagythj4 132 22 , , , work_53xuaunsqfhv7cuuzotagythj4 132 23 1997 1997 CD work_53xuaunsqfhv7cuuzotagythj4 132 24 . . . work_53xuaunsqfhv7cuuzotagythj4 133 1 Golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 133 2 Ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 133 3 : : : work_53xuaunsqfhv7cuuzotagythj4 133 4 The the DT work_53xuaunsqfhv7cuuzotagythj4 133 5 Mathematics Mathematics NNPS work_53xuaunsqfhv7cuuzotagythj4 133 6 of of IN work_53xuaunsqfhv7cuuzotagythj4 133 7 Beauty Beauty NNP work_53xuaunsqfhv7cuuzotagythj4 133 8 9 9 CD work_53xuaunsqfhv7cuuzotagythj4 133 9 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 133 10 5 5 CD work_53xuaunsqfhv7cuuzotagythj4 133 11 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 133 12 U. U. NNP work_53xuaunsqfhv7cuuzotagythj4 133 13 Eco Eco NNP work_53xuaunsqfhv7cuuzotagythj4 133 14 , , , work_53xuaunsqfhv7cuuzotagythj4 133 15 Art Art NNP work_53xuaunsqfhv7cuuzotagythj4 133 16 and and CC work_53xuaunsqfhv7cuuzotagythj4 133 17 Beauty beauty NN work_53xuaunsqfhv7cuuzotagythj4 133 18 in in IN work_53xuaunsqfhv7cuuzotagythj4 133 19 the the DT work_53xuaunsqfhv7cuuzotagythj4 133 20 Middle Middle NNP work_53xuaunsqfhv7cuuzotagythj4 133 21 Ages Ages NNPS work_53xuaunsqfhv7cuuzotagythj4 133 22 , , , work_53xuaunsqfhv7cuuzotagythj4 133 23 Translated translate VBN work_53xuaunsqfhv7cuuzotagythj4 133 24 by by IN work_53xuaunsqfhv7cuuzotagythj4 133 25 H. H. NNP work_53xuaunsqfhv7cuuzotagythj4 133 26 Bredin Bredin NNP work_53xuaunsqfhv7cuuzotagythj4 133 27 , , , work_53xuaunsqfhv7cuuzotagythj4 133 28 Yale Yale NNP work_53xuaunsqfhv7cuuzotagythj4 133 29 University University NNP work_53xuaunsqfhv7cuuzotagythj4 133 30 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 133 31 , , , work_53xuaunsqfhv7cuuzotagythj4 133 32 New New NNP work_53xuaunsqfhv7cuuzotagythj4 133 33 Haven Haven NNP work_53xuaunsqfhv7cuuzotagythj4 133 34 , , , work_53xuaunsqfhv7cuuzotagythj4 133 35 2002 2002 CD work_53xuaunsqfhv7cuuzotagythj4 133 36 . . . work_53xuaunsqfhv7cuuzotagythj4 134 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 134 2 6 6 CD work_53xuaunsqfhv7cuuzotagythj4 134 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 134 4 K. K. NNP work_53xuaunsqfhv7cuuzotagythj4 134 5 Fink Fink NNP work_53xuaunsqfhv7cuuzotagythj4 134 6 , , , work_53xuaunsqfhv7cuuzotagythj4 134 7 W. W. NNP work_53xuaunsqfhv7cuuzotagythj4 134 8 W. W. NNP work_53xuaunsqfhv7cuuzotagythj4 134 9 Beman Beman NNP work_53xuaunsqfhv7cuuzotagythj4 134 10 and and CC work_53xuaunsqfhv7cuuzotagythj4 134 11 D. D. NNP work_53xuaunsqfhv7cuuzotagythj4 134 12 E. E. NNP work_53xuaunsqfhv7cuuzotagythj4 134 13 Smith Smith NNP work_53xuaunsqfhv7cuuzotagythj4 134 14 , , , work_53xuaunsqfhv7cuuzotagythj4 134 15 A a DT work_53xuaunsqfhv7cuuzotagythj4 134 16 Brief brief JJ work_53xuaunsqfhv7cuuzotagythj4 134 17 History history NN work_53xuaunsqfhv7cuuzotagythj4 134 18 of of IN work_53xuaunsqfhv7cuuzotagythj4 134 19 Mathemat- Mathemat- NNP work_53xuaunsqfhv7cuuzotagythj4 134 20 ics ics NN work_53xuaunsqfhv7cuuzotagythj4 134 21 : : : work_53xuaunsqfhv7cuuzotagythj4 134 22 An an DT work_53xuaunsqfhv7cuuzotagythj4 134 23 Authorized Authorized NNP work_53xuaunsqfhv7cuuzotagythj4 134 24 Translation translation NN work_53xuaunsqfhv7cuuzotagythj4 134 25 of of IN work_53xuaunsqfhv7cuuzotagythj4 134 26 Dr. Dr. NNP work_53xuaunsqfhv7cuuzotagythj4 134 27 Karl Karl NNP work_53xuaunsqfhv7cuuzotagythj4 134 28 Fink Fink NNP work_53xuaunsqfhv7cuuzotagythj4 134 29 ’s ’s POS work_53xuaunsqfhv7cuuzotagythj4 134 30 Geschichte Geschichte NNP work_53xuaunsqfhv7cuuzotagythj4 134 31 der der VBD work_53xuaunsqfhv7cuuzotagythj4 134 32 Elementar- Elementar- NNP work_53xuaunsqfhv7cuuzotagythj4 134 33 Mathematik Mathematik NNP work_53xuaunsqfhv7cuuzotagythj4 134 34 , , , work_53xuaunsqfhv7cuuzotagythj4 134 35 The the DT work_53xuaunsqfhv7cuuzotagythj4 134 36 Open Open NNP work_53xuaunsqfhv7cuuzotagythj4 134 37 Court Court NNP work_53xuaunsqfhv7cuuzotagythj4 134 38 Pub Pub NNP work_53xuaunsqfhv7cuuzotagythj4 134 39 . . . work_53xuaunsqfhv7cuuzotagythj4 135 1 Co. Co. NNP work_53xuaunsqfhv7cuuzotagythj4 135 2 , , , work_53xuaunsqfhv7cuuzotagythj4 135 3 Chicago Chicago NNP work_53xuaunsqfhv7cuuzotagythj4 135 4 , , , work_53xuaunsqfhv7cuuzotagythj4 135 5 1900 1900 CD work_53xuaunsqfhv7cuuzotagythj4 135 6 . . . work_53xuaunsqfhv7cuuzotagythj4 136 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 136 2 7 7 CD work_53xuaunsqfhv7cuuzotagythj4 136 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 136 4 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 136 5 Herz Herz NNP work_53xuaunsqfhv7cuuzotagythj4 136 6 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 136 7 Fischler Fischler NNP work_53xuaunsqfhv7cuuzotagythj4 136 8 , , , work_53xuaunsqfhv7cuuzotagythj4 136 9 The the DT work_53xuaunsqfhv7cuuzotagythj4 136 10 Shape Shape NNP work_53xuaunsqfhv7cuuzotagythj4 136 11 of of IN work_53xuaunsqfhv7cuuzotagythj4 136 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 136 13 Great Great NNP work_53xuaunsqfhv7cuuzotagythj4 136 14 Pyramid Pyramid NNP work_53xuaunsqfhv7cuuzotagythj4 136 15 , , , work_53xuaunsqfhv7cuuzotagythj4 136 16 Wilfrid Wilfrid NNP work_53xuaunsqfhv7cuuzotagythj4 136 17 Laurier Laurier NNP work_53xuaunsqfhv7cuuzotagythj4 136 18 University University NNP work_53xuaunsqfhv7cuuzotagythj4 136 19 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 136 20 , , , work_53xuaunsqfhv7cuuzotagythj4 136 21 Waterloo Waterloo NNP work_53xuaunsqfhv7cuuzotagythj4 136 22 , , , work_53xuaunsqfhv7cuuzotagythj4 136 23 2000 2000 CD work_53xuaunsqfhv7cuuzotagythj4 136 24 . . . work_53xuaunsqfhv7cuuzotagythj4 137 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 137 2 8 8 CD work_53xuaunsqfhv7cuuzotagythj4 137 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 137 4 G. G. NNP work_53xuaunsqfhv7cuuzotagythj4 137 5 H. H. NNP work_53xuaunsqfhv7cuuzotagythj4 137 6 Hardy Hardy NNP work_53xuaunsqfhv7cuuzotagythj4 137 7 and and CC work_53xuaunsqfhv7cuuzotagythj4 137 8 E. E. NNP work_53xuaunsqfhv7cuuzotagythj4 137 9 M. M. NNP work_53xuaunsqfhv7cuuzotagythj4 137 10 Wright Wright NNP work_53xuaunsqfhv7cuuzotagythj4 137 11 , , , work_53xuaunsqfhv7cuuzotagythj4 137 12 An an DT work_53xuaunsqfhv7cuuzotagythj4 137 13 Introduction introduction NN work_53xuaunsqfhv7cuuzotagythj4 137 14 to to IN work_53xuaunsqfhv7cuuzotagythj4 137 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 137 16 Theory Theory NNP work_53xuaunsqfhv7cuuzotagythj4 137 17 of of IN work_53xuaunsqfhv7cuuzotagythj4 137 18 Numbers Numbers NNPS work_53xuaunsqfhv7cuuzotagythj4 137 19 , , , work_53xuaunsqfhv7cuuzotagythj4 137 20 Fifth fifth JJ work_53xuaunsqfhv7cuuzotagythj4 137 21 edition edition NN work_53xuaunsqfhv7cuuzotagythj4 137 22 . . . work_53xuaunsqfhv7cuuzotagythj4 138 1 The the DT work_53xuaunsqfhv7cuuzotagythj4 138 2 Clarendon Clarendon NNP work_53xuaunsqfhv7cuuzotagythj4 138 3 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 138 4 , , , work_53xuaunsqfhv7cuuzotagythj4 138 5 Oxford Oxford NNP work_53xuaunsqfhv7cuuzotagythj4 138 6 University University NNP work_53xuaunsqfhv7cuuzotagythj4 138 7 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 138 8 , , , work_53xuaunsqfhv7cuuzotagythj4 138 9 New New NNP work_53xuaunsqfhv7cuuzotagythj4 138 10 York York NNP work_53xuaunsqfhv7cuuzotagythj4 138 11 , , , work_53xuaunsqfhv7cuuzotagythj4 138 12 1979 1979 CD work_53xuaunsqfhv7cuuzotagythj4 138 13 . . . work_53xuaunsqfhv7cuuzotagythj4 139 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 139 2 9 9 CD work_53xuaunsqfhv7cuuzotagythj4 139 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 139 4 G. G. NNP work_53xuaunsqfhv7cuuzotagythj4 139 5 L. L. NNP work_53xuaunsqfhv7cuuzotagythj4 139 6 Hersey Hersey NNP work_53xuaunsqfhv7cuuzotagythj4 139 7 , , , work_53xuaunsqfhv7cuuzotagythj4 139 8 Architecture Architecture NNP work_53xuaunsqfhv7cuuzotagythj4 139 9 and and CC work_53xuaunsqfhv7cuuzotagythj4 139 10 Geometry Geometry NNP work_53xuaunsqfhv7cuuzotagythj4 139 11 in in IN work_53xuaunsqfhv7cuuzotagythj4 139 12 the the DT work_53xuaunsqfhv7cuuzotagythj4 139 13 Age Age NNP work_53xuaunsqfhv7cuuzotagythj4 139 14 of of IN work_53xuaunsqfhv7cuuzotagythj4 139 15 the the DT work_53xuaunsqfhv7cuuzotagythj4 139 16 Baroque Baroque NNP work_53xuaunsqfhv7cuuzotagythj4 139 17 , , , work_53xuaunsqfhv7cuuzotagythj4 139 18 The the DT work_53xuaunsqfhv7cuuzotagythj4 139 19 University University NNP work_53xuaunsqfhv7cuuzotagythj4 139 20 of of IN work_53xuaunsqfhv7cuuzotagythj4 139 21 Chicago Chicago NNP work_53xuaunsqfhv7cuuzotagythj4 139 22 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 139 23 , , , work_53xuaunsqfhv7cuuzotagythj4 139 24 Chicago Chicago NNP work_53xuaunsqfhv7cuuzotagythj4 139 25 , , , work_53xuaunsqfhv7cuuzotagythj4 139 26 2002 2002 CD work_53xuaunsqfhv7cuuzotagythj4 139 27 . . . work_53xuaunsqfhv7cuuzotagythj4 140 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 140 2 10 10 CD work_53xuaunsqfhv7cuuzotagythj4 140 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 140 4 M. M. NNP work_53xuaunsqfhv7cuuzotagythj4 140 5 Hejazi Hejazi NNP work_53xuaunsqfhv7cuuzotagythj4 140 6 , , , work_53xuaunsqfhv7cuuzotagythj4 140 7 Geometry Geometry NNP work_53xuaunsqfhv7cuuzotagythj4 140 8 in in IN work_53xuaunsqfhv7cuuzotagythj4 140 9 nature nature NN work_53xuaunsqfhv7cuuzotagythj4 140 10 and and CC work_53xuaunsqfhv7cuuzotagythj4 140 11 Persian persian JJ work_53xuaunsqfhv7cuuzotagythj4 140 12 architecture architecture NN work_53xuaunsqfhv7cuuzotagythj4 140 13 , , , work_53xuaunsqfhv7cuuzotagythj4 140 14 Build Build NNP work_53xuaunsqfhv7cuuzotagythj4 140 15 . . . work_53xuaunsqfhv7cuuzotagythj4 141 1 Environ Environ NNP work_53xuaunsqfhv7cuuzotagythj4 141 2 . . . work_53xuaunsqfhv7cuuzotagythj4 142 1 40 40 CD work_53xuaunsqfhv7cuuzotagythj4 142 2 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 142 3 2005 2005 CD work_53xuaunsqfhv7cuuzotagythj4 142 4 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 142 5 1413 1413 CD work_53xuaunsqfhv7cuuzotagythj4 142 6 − − NNP work_53xuaunsqfhv7cuuzotagythj4 142 7 1427 1427 CD work_53xuaunsqfhv7cuuzotagythj4 142 8 . . . work_53xuaunsqfhv7cuuzotagythj4 143 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 143 2 11 11 CD work_53xuaunsqfhv7cuuzotagythj4 143 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 143 4 M. M. NNP work_53xuaunsqfhv7cuuzotagythj4 143 5 Hejazi Hejazi NNP work_53xuaunsqfhv7cuuzotagythj4 143 6 and and CC work_53xuaunsqfhv7cuuzotagythj4 143 7 F. F. NNP work_53xuaunsqfhv7cuuzotagythj4 143 8 Mehdizadeh Mehdizadeh NNP work_53xuaunsqfhv7cuuzotagythj4 143 9 Saradj Saradj NNP work_53xuaunsqfhv7cuuzotagythj4 143 10 , , , work_53xuaunsqfhv7cuuzotagythj4 143 11 Persian Persian NNP work_53xuaunsqfhv7cuuzotagythj4 143 12 Architectural Architectural NNP work_53xuaunsqfhv7cuuzotagythj4 143 13 Heritage Heritage NNP work_53xuaunsqfhv7cuuzotagythj4 143 14 : : : work_53xuaunsqfhv7cuuzotagythj4 143 15 Archi- archi- NN work_53xuaunsqfhv7cuuzotagythj4 143 16 tecture tecture NN work_53xuaunsqfhv7cuuzotagythj4 143 17 , , , work_53xuaunsqfhv7cuuzotagythj4 143 18 Structure Structure NNP work_53xuaunsqfhv7cuuzotagythj4 143 19 and and CC work_53xuaunsqfhv7cuuzotagythj4 143 20 Conservation Conservation NNP work_53xuaunsqfhv7cuuzotagythj4 143 21 , , , work_53xuaunsqfhv7cuuzotagythj4 143 22 WIT WIT NNP work_53xuaunsqfhv7cuuzotagythj4 143 23 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 143 24 , , , work_53xuaunsqfhv7cuuzotagythj4 143 25 Southampton Southampton NNP work_53xuaunsqfhv7cuuzotagythj4 143 26 , , , work_53xuaunsqfhv7cuuzotagythj4 143 27 2014 2014 CD work_53xuaunsqfhv7cuuzotagythj4 143 28 . . . work_53xuaunsqfhv7cuuzotagythj4 144 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 144 2 12 12 CD work_53xuaunsqfhv7cuuzotagythj4 144 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 144 4 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 144 5 V. V. NNP work_53xuaunsqfhv7cuuzotagythj4 144 6 Jean Jean NNP work_53xuaunsqfhv7cuuzotagythj4 144 7 , , , work_53xuaunsqfhv7cuuzotagythj4 144 8 Phyllotaxis Phyllotaxis NNP work_53xuaunsqfhv7cuuzotagythj4 144 9 : : : work_53xuaunsqfhv7cuuzotagythj4 144 10 A a DT work_53xuaunsqfhv7cuuzotagythj4 144 11 Systemic Systemic NNP work_53xuaunsqfhv7cuuzotagythj4 144 12 Study Study NNP work_53xuaunsqfhv7cuuzotagythj4 144 13 in in IN work_53xuaunsqfhv7cuuzotagythj4 144 14 Plant Plant NNP work_53xuaunsqfhv7cuuzotagythj4 144 15 Morphogenesis Morphogenesis NNP work_53xuaunsqfhv7cuuzotagythj4 144 16 , , , work_53xuaunsqfhv7cuuzotagythj4 144 17 Cam- Cam- NNP work_53xuaunsqfhv7cuuzotagythj4 144 18 bridge bridge NN work_53xuaunsqfhv7cuuzotagythj4 144 19 University University NNP work_53xuaunsqfhv7cuuzotagythj4 144 20 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 144 21 , , , work_53xuaunsqfhv7cuuzotagythj4 144 22 Cambridge Cambridge NNP work_53xuaunsqfhv7cuuzotagythj4 144 23 , , , work_53xuaunsqfhv7cuuzotagythj4 144 24 1994 1994 CD work_53xuaunsqfhv7cuuzotagythj4 144 25 . . . work_53xuaunsqfhv7cuuzotagythj4 145 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 145 2 13 13 CD work_53xuaunsqfhv7cuuzotagythj4 145 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 145 4 S. S. NNP work_53xuaunsqfhv7cuuzotagythj4 145 5 Iwamoto Iwamoto NNP work_53xuaunsqfhv7cuuzotagythj4 145 6 and and CC work_53xuaunsqfhv7cuuzotagythj4 145 7 K. K. NNP work_53xuaunsqfhv7cuuzotagythj4 145 8 Akifumi Akifumi NNP work_53xuaunsqfhv7cuuzotagythj4 145 9 , , , work_53xuaunsqfhv7cuuzotagythj4 145 10 On on IN work_53xuaunsqfhv7cuuzotagythj4 145 11 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 145 12 inequalities inequality NNS work_53xuaunsqfhv7cuuzotagythj4 145 13 , , , work_53xuaunsqfhv7cuuzotagythj4 145 14 1504 1504 CD work_53xuaunsqfhv7cuuzotagythj4 145 15 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 145 16 2006 2006 CD work_53xuaunsqfhv7cuuzotagythj4 145 17 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 145 18 168 168 CD work_53xuaunsqfhv7cuuzotagythj4 145 19 − − NNP work_53xuaunsqfhv7cuuzotagythj4 145 20 176 176 CD work_53xuaunsqfhv7cuuzotagythj4 145 21 . . . work_53xuaunsqfhv7cuuzotagythj4 146 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 146 2 14 14 CD work_53xuaunsqfhv7cuuzotagythj4 146 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 146 4 J. J. NNP work_53xuaunsqfhv7cuuzotagythj4 146 5 Kappraff Kappraff NNP work_53xuaunsqfhv7cuuzotagythj4 146 6 , , , work_53xuaunsqfhv7cuuzotagythj4 146 7 A a DT work_53xuaunsqfhv7cuuzotagythj4 146 8 course course NN work_53xuaunsqfhv7cuuzotagythj4 146 9 in in IN work_53xuaunsqfhv7cuuzotagythj4 146 10 the the DT work_53xuaunsqfhv7cuuzotagythj4 146 11 mathematics mathematic NNS work_53xuaunsqfhv7cuuzotagythj4 146 12 of of IN work_53xuaunsqfhv7cuuzotagythj4 146 13 design design NN work_53xuaunsqfhv7cuuzotagythj4 146 14 , , , work_53xuaunsqfhv7cuuzotagythj4 146 15 Comput comput NN work_53xuaunsqfhv7cuuzotagythj4 146 16 . . . work_53xuaunsqfhv7cuuzotagythj4 147 1 Math math NN work_53xuaunsqfhv7cuuzotagythj4 147 2 . . . work_53xuaunsqfhv7cuuzotagythj4 148 1 Appl Appl NNP work_53xuaunsqfhv7cuuzotagythj4 148 2 . . . work_53xuaunsqfhv7cuuzotagythj4 149 1 12(3 12(3 LS work_53xuaunsqfhv7cuuzotagythj4 149 2 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 149 3 4)(Part 4)(part CD work_53xuaunsqfhv7cuuzotagythj4 149 4 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 149 5 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 149 6 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 149 7 1986 1986 CD work_53xuaunsqfhv7cuuzotagythj4 149 8 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 149 9 913 913 CD work_53xuaunsqfhv7cuuzotagythj4 149 10 − − NNP work_53xuaunsqfhv7cuuzotagythj4 149 11 948 948 CD work_53xuaunsqfhv7cuuzotagythj4 149 12 . . . work_53xuaunsqfhv7cuuzotagythj4 150 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 150 2 15 15 CD work_53xuaunsqfhv7cuuzotagythj4 150 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 150 4 D. D. NNP work_53xuaunsqfhv7cuuzotagythj4 150 5 E. E. NNP work_53xuaunsqfhv7cuuzotagythj4 150 6 Knuth Knuth NNP work_53xuaunsqfhv7cuuzotagythj4 150 7 , , , work_53xuaunsqfhv7cuuzotagythj4 150 8 The the DT work_53xuaunsqfhv7cuuzotagythj4 150 9 Art Art NNP work_53xuaunsqfhv7cuuzotagythj4 150 10 of of IN work_53xuaunsqfhv7cuuzotagythj4 150 11 Computer Computer NNP work_53xuaunsqfhv7cuuzotagythj4 150 12 Programming Programming NNP work_53xuaunsqfhv7cuuzotagythj4 150 13 , , , work_53xuaunsqfhv7cuuzotagythj4 150 14 Volume volume NN work_53xuaunsqfhv7cuuzotagythj4 150 15 2 2 CD work_53xuaunsqfhv7cuuzotagythj4 150 16 : : : work_53xuaunsqfhv7cuuzotagythj4 150 17 Seminumerical Seminumerical NNP work_53xuaunsqfhv7cuuzotagythj4 150 18 Algorithms Algorithms NNP work_53xuaunsqfhv7cuuzotagythj4 150 19 , , , work_53xuaunsqfhv7cuuzotagythj4 150 20 Addison Addison NNP work_53xuaunsqfhv7cuuzotagythj4 150 21 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 150 22 Wesley Wesley NNP work_53xuaunsqfhv7cuuzotagythj4 150 23 Professional Professional NNP work_53xuaunsqfhv7cuuzotagythj4 150 24 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 150 25 , , , work_53xuaunsqfhv7cuuzotagythj4 150 26 Massachusetts Massachusetts NNP work_53xuaunsqfhv7cuuzotagythj4 150 27 , , , work_53xuaunsqfhv7cuuzotagythj4 150 28 1997 1997 CD work_53xuaunsqfhv7cuuzotagythj4 150 29 . . . work_53xuaunsqfhv7cuuzotagythj4 151 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 151 2 16 16 CD work_53xuaunsqfhv7cuuzotagythj4 151 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 151 4 M. M. NNP work_53xuaunsqfhv7cuuzotagythj4 151 5 Livio Livio NNP work_53xuaunsqfhv7cuuzotagythj4 151 6 , , , work_53xuaunsqfhv7cuuzotagythj4 151 7 The the DT work_53xuaunsqfhv7cuuzotagythj4 151 8 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 151 9 Ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 151 10 : : : work_53xuaunsqfhv7cuuzotagythj4 151 11 The The NNP work_53xuaunsqfhv7cuuzotagythj4 151 12 Story Story NNP work_53xuaunsqfhv7cuuzotagythj4 151 13 of of IN work_53xuaunsqfhv7cuuzotagythj4 151 14 Phi Phi NNP work_53xuaunsqfhv7cuuzotagythj4 151 15 , , , work_53xuaunsqfhv7cuuzotagythj4 151 16 the the DT work_53xuaunsqfhv7cuuzotagythj4 151 17 World World NNP work_53xuaunsqfhv7cuuzotagythj4 151 18 ’s ’s POS work_53xuaunsqfhv7cuuzotagythj4 151 19 Most Most NNP work_53xuaunsqfhv7cuuzotagythj4 151 20 Astonishing Astonishing NNP work_53xuaunsqfhv7cuuzotagythj4 151 21 Number Number NNP work_53xuaunsqfhv7cuuzotagythj4 151 22 , , , work_53xuaunsqfhv7cuuzotagythj4 151 23 Broadway Broadway NNP work_53xuaunsqfhv7cuuzotagythj4 151 24 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 151 25 , , , work_53xuaunsqfhv7cuuzotagythj4 151 26 New New NNP work_53xuaunsqfhv7cuuzotagythj4 151 27 York York NNP work_53xuaunsqfhv7cuuzotagythj4 151 28 , , , work_53xuaunsqfhv7cuuzotagythj4 151 29 2008 2008 CD work_53xuaunsqfhv7cuuzotagythj4 151 30 . . . work_53xuaunsqfhv7cuuzotagythj4 152 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 152 2 17 17 CD work_53xuaunsqfhv7cuuzotagythj4 152 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 152 4 N. N. NNP work_53xuaunsqfhv7cuuzotagythj4 152 5 A. a. NN work_53xuaunsqfhv7cuuzotagythj4 152 6 Megahed Megahed NNP work_53xuaunsqfhv7cuuzotagythj4 152 7 , , , work_53xuaunsqfhv7cuuzotagythj4 152 8 Towards towards IN work_53xuaunsqfhv7cuuzotagythj4 152 9 math math NN work_53xuaunsqfhv7cuuzotagythj4 152 10 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 152 11 based base VBN work_53xuaunsqfhv7cuuzotagythj4 152 12 architectural architectural JJ work_53xuaunsqfhv7cuuzotagythj4 152 13 education education NN work_53xuaunsqfhv7cuuzotagythj4 152 14 in in IN work_53xuaunsqfhv7cuuzotagythj4 152 15 Egyptian egyptian JJ work_53xuaunsqfhv7cuuzotagythj4 152 16 engineering engineering NN work_53xuaunsqfhv7cuuzotagythj4 152 17 faculties faculty NNS work_53xuaunsqfhv7cuuzotagythj4 152 18 , , , work_53xuaunsqfhv7cuuzotagythj4 152 19 Nexus Nexus NNP work_53xuaunsqfhv7cuuzotagythj4 152 20 Netw Netw NNP work_53xuaunsqfhv7cuuzotagythj4 152 21 . . . work_53xuaunsqfhv7cuuzotagythj4 153 1 J. J. NNP work_53xuaunsqfhv7cuuzotagythj4 154 1 15(3 15(3 LS work_53xuaunsqfhv7cuuzotagythj4 154 2 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 154 3 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 154 4 2013 2013 CD work_53xuaunsqfhv7cuuzotagythj4 154 5 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 154 6 565 565 CD work_53xuaunsqfhv7cuuzotagythj4 154 7 − − NNP work_53xuaunsqfhv7cuuzotagythj4 154 8 581 581 CD work_53xuaunsqfhv7cuuzotagythj4 154 9 . . . work_53xuaunsqfhv7cuuzotagythj4 155 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 155 2 18 18 CD work_53xuaunsqfhv7cuuzotagythj4 155 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 155 4 F. F. NNP work_53xuaunsqfhv7cuuzotagythj4 155 5 Nabavi Nabavi NNP work_53xuaunsqfhv7cuuzotagythj4 155 6 and and CC work_53xuaunsqfhv7cuuzotagythj4 155 7 Y. Y. NNP work_53xuaunsqfhv7cuuzotagythj4 155 8 Ahmad Ahmad NNP work_53xuaunsqfhv7cuuzotagythj4 155 9 , , , work_53xuaunsqfhv7cuuzotagythj4 155 10 Is be VBZ work_53xuaunsqfhv7cuuzotagythj4 155 11 there there EX work_53xuaunsqfhv7cuuzotagythj4 155 12 any any DT work_53xuaunsqfhv7cuuzotagythj4 155 13 geometrical geometrical JJ work_53xuaunsqfhv7cuuzotagythj4 155 14 golden golden JJ work_53xuaunsqfhv7cuuzotagythj4 155 15 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 155 16 in in IN work_53xuaunsqfhv7cuuzotagythj4 155 17 tradi- tradi- JJ work_53xuaunsqfhv7cuuzotagythj4 155 18 tional tional JJ work_53xuaunsqfhv7cuuzotagythj4 155 19 Iranian iranian JJ work_53xuaunsqfhv7cuuzotagythj4 155 20 courtyard courtyard NN work_53xuaunsqfhv7cuuzotagythj4 155 21 houses house NNS work_53xuaunsqfhv7cuuzotagythj4 155 22 , , , work_53xuaunsqfhv7cuuzotagythj4 155 23 International International NNP work_53xuaunsqfhv7cuuzotagythj4 155 24 Journal Journal NNP work_53xuaunsqfhv7cuuzotagythj4 155 25 of of IN work_53xuaunsqfhv7cuuzotagythj4 155 26 Architectural Architectural NNP work_53xuaunsqfhv7cuuzotagythj4 155 27 Re- Re- NNP work_53xuaunsqfhv7cuuzotagythj4 155 28 search search NN work_53xuaunsqfhv7cuuzotagythj4 155 29 10(1 10(1 CD work_53xuaunsqfhv7cuuzotagythj4 155 30 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 155 31 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 155 32 2016 2016 CD work_53xuaunsqfhv7cuuzotagythj4 155 33 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 155 34 143 143 CD work_53xuaunsqfhv7cuuzotagythj4 155 35 − − NNP work_53xuaunsqfhv7cuuzotagythj4 155 36 154 154 CD work_53xuaunsqfhv7cuuzotagythj4 155 37 . . . work_53xuaunsqfhv7cuuzotagythj4 156 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 156 2 19 19 CD work_53xuaunsqfhv7cuuzotagythj4 156 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 156 4 P. P. NNP work_53xuaunsqfhv7cuuzotagythj4 156 5 Prusinkiewicz Prusinkiewicz NNP work_53xuaunsqfhv7cuuzotagythj4 156 6 and and CC work_53xuaunsqfhv7cuuzotagythj4 156 7 A. A. NNP work_53xuaunsqfhv7cuuzotagythj4 156 8 Lindenmayer Lindenmayer NNP work_53xuaunsqfhv7cuuzotagythj4 156 9 , , , work_53xuaunsqfhv7cuuzotagythj4 156 10 The the DT work_53xuaunsqfhv7cuuzotagythj4 156 11 Algorithmic Algorithmic NNP work_53xuaunsqfhv7cuuzotagythj4 156 12 Beauty Beauty NNP work_53xuaunsqfhv7cuuzotagythj4 156 13 of of IN work_53xuaunsqfhv7cuuzotagythj4 156 14 Plants Plants NNPS work_53xuaunsqfhv7cuuzotagythj4 156 15 , , , work_53xuaunsqfhv7cuuzotagythj4 156 16 Springer Springer NNP work_53xuaunsqfhv7cuuzotagythj4 156 17 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 156 18 Verlag Verlag NNP work_53xuaunsqfhv7cuuzotagythj4 156 19 , , , work_53xuaunsqfhv7cuuzotagythj4 156 20 New New NNP work_53xuaunsqfhv7cuuzotagythj4 156 21 York York NNP work_53xuaunsqfhv7cuuzotagythj4 156 22 , , , work_53xuaunsqfhv7cuuzotagythj4 156 23 2004 2004 CD work_53xuaunsqfhv7cuuzotagythj4 156 24 . . . work_53xuaunsqfhv7cuuzotagythj4 157 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 157 2 20 20 CD work_53xuaunsqfhv7cuuzotagythj4 157 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 157 4 A. a. NN work_53xuaunsqfhv7cuuzotagythj4 157 5 Samalavičius Samalavičius NNP work_53xuaunsqfhv7cuuzotagythj4 157 6 , , , work_53xuaunsqfhv7cuuzotagythj4 157 7 Ideas Ideas NNPS work_53xuaunsqfhv7cuuzotagythj4 157 8 and and CC work_53xuaunsqfhv7cuuzotagythj4 157 9 Structures Structures NNPS work_53xuaunsqfhv7cuuzotagythj4 157 10 : : : work_53xuaunsqfhv7cuuzotagythj4 157 11 Essays essay NNS work_53xuaunsqfhv7cuuzotagythj4 157 12 in in IN work_53xuaunsqfhv7cuuzotagythj4 157 13 Architectural Architectural NNP work_53xuaunsqfhv7cuuzotagythj4 157 14 History History NNP work_53xuaunsqfhv7cuuzotagythj4 157 15 , , , work_53xuaunsqfhv7cuuzotagythj4 157 16 Eu- Eu- NNP work_53xuaunsqfhv7cuuzotagythj4 157 17 gene gene NN work_53xuaunsqfhv7cuuzotagythj4 157 18 , , , work_53xuaunsqfhv7cuuzotagythj4 157 19 Oregon Oregon NNP work_53xuaunsqfhv7cuuzotagythj4 157 20 : : : work_53xuaunsqfhv7cuuzotagythj4 157 21 Resource Resource NNP work_53xuaunsqfhv7cuuzotagythj4 157 22 Publications Publications NNPS work_53xuaunsqfhv7cuuzotagythj4 157 23 / / SYM work_53xuaunsqfhv7cuuzotagythj4 157 24 An an DT work_53xuaunsqfhv7cuuzotagythj4 157 25 Imprint Imprint NNP work_53xuaunsqfhv7cuuzotagythj4 157 26 of of IN work_53xuaunsqfhv7cuuzotagythj4 157 27 Wipf Wipf NNP work_53xuaunsqfhv7cuuzotagythj4 157 28 and and CC work_53xuaunsqfhv7cuuzotagythj4 157 29 Stock Stock NNP work_53xuaunsqfhv7cuuzotagythj4 157 30 Publish- Publish- NNP work_53xuaunsqfhv7cuuzotagythj4 157 31 ers er NNS work_53xuaunsqfhv7cuuzotagythj4 157 32 , , , work_53xuaunsqfhv7cuuzotagythj4 157 33 Portland Portland NNP work_53xuaunsqfhv7cuuzotagythj4 157 34 , , , work_53xuaunsqfhv7cuuzotagythj4 157 35 2011 2011 CD work_53xuaunsqfhv7cuuzotagythj4 157 36 . . . work_53xuaunsqfhv7cuuzotagythj4 158 1 10 10 CD work_53xuaunsqfhv7cuuzotagythj4 158 2 Hamid Hamid NNP work_53xuaunsqfhv7cuuzotagythj4 158 3 Ghorbani Ghorbani NNP work_53xuaunsqfhv7cuuzotagythj4 158 4 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 158 5 21 21 CD work_53xuaunsqfhv7cuuzotagythj4 158 6 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 158 7 S. S. NNP work_53xuaunsqfhv7cuuzotagythj4 158 8 K. K. NNP work_53xuaunsqfhv7cuuzotagythj4 158 9 Sen Sen NNP work_53xuaunsqfhv7cuuzotagythj4 158 10 and and CC work_53xuaunsqfhv7cuuzotagythj4 158 11 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 158 12 P. P. NNP work_53xuaunsqfhv7cuuzotagythj4 158 13 Agarwal Agarwal NNP work_53xuaunsqfhv7cuuzotagythj4 158 14 , , , work_53xuaunsqfhv7cuuzotagythj4 158 15 Golden Golden NNP work_53xuaunsqfhv7cuuzotagythj4 158 16 ratio ratio NN work_53xuaunsqfhv7cuuzotagythj4 158 17 in in IN work_53xuaunsqfhv7cuuzotagythj4 158 18 science science NN work_53xuaunsqfhv7cuuzotagythj4 158 19 , , , work_53xuaunsqfhv7cuuzotagythj4 158 20 as as IN work_53xuaunsqfhv7cuuzotagythj4 158 21 random random JJ work_53xuaunsqfhv7cuuzotagythj4 158 22 sequence sequence NN work_53xuaunsqfhv7cuuzotagythj4 158 23 source source NN work_53xuaunsqfhv7cuuzotagythj4 158 24 , , , work_53xuaunsqfhv7cuuzotagythj4 158 25 its -PRON- PRP$ work_53xuaunsqfhv7cuuzotagythj4 158 26 computation computation NN work_53xuaunsqfhv7cuuzotagythj4 158 27 and and CC work_53xuaunsqfhv7cuuzotagythj4 158 28 beyond beyond IN work_53xuaunsqfhv7cuuzotagythj4 158 29 , , , work_53xuaunsqfhv7cuuzotagythj4 158 30 Comput Comput NNP work_53xuaunsqfhv7cuuzotagythj4 158 31 . . . work_53xuaunsqfhv7cuuzotagythj4 159 1 Math math NN work_53xuaunsqfhv7cuuzotagythj4 159 2 . . . work_53xuaunsqfhv7cuuzotagythj4 160 1 Appl Appl NNP work_53xuaunsqfhv7cuuzotagythj4 160 2 . . . work_53xuaunsqfhv7cuuzotagythj4 161 1 56(2 56(2 CD work_53xuaunsqfhv7cuuzotagythj4 161 2 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 161 3 ( ( -LRB- work_53xuaunsqfhv7cuuzotagythj4 161 4 2008 2008 CD work_53xuaunsqfhv7cuuzotagythj4 161 5 ) ) -RRB- work_53xuaunsqfhv7cuuzotagythj4 161 6 469− 469− NNP work_53xuaunsqfhv7cuuzotagythj4 161 7 498 498 CD work_53xuaunsqfhv7cuuzotagythj4 161 8 . . . work_53xuaunsqfhv7cuuzotagythj4 162 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 162 2 22 22 CD work_53xuaunsqfhv7cuuzotagythj4 162 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 162 4 I. 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NNP work_53xuaunsqfhv7cuuzotagythj4 162 5 Stewart Stewart NNP work_53xuaunsqfhv7cuuzotagythj4 162 6 , , , work_53xuaunsqfhv7cuuzotagythj4 162 7 Nature Nature NNP work_53xuaunsqfhv7cuuzotagythj4 162 8 ’s ’s POS work_53xuaunsqfhv7cuuzotagythj4 162 9 Numbers number NNS work_53xuaunsqfhv7cuuzotagythj4 162 10 : : : work_53xuaunsqfhv7cuuzotagythj4 162 11 The the DT work_53xuaunsqfhv7cuuzotagythj4 162 12 Unreal Unreal NNP work_53xuaunsqfhv7cuuzotagythj4 162 13 Reality Reality NNP work_53xuaunsqfhv7cuuzotagythj4 162 14 of of IN work_53xuaunsqfhv7cuuzotagythj4 162 15 Mathematics Mathematics NNPS work_53xuaunsqfhv7cuuzotagythj4 162 16 , , , work_53xuaunsqfhv7cuuzotagythj4 162 17 Basic- Basic- NNP work_53xuaunsqfhv7cuuzotagythj4 162 18 Books Books NNP work_53xuaunsqfhv7cuuzotagythj4 162 19 Press Press NNP work_53xuaunsqfhv7cuuzotagythj4 162 20 , , , work_53xuaunsqfhv7cuuzotagythj4 162 21 New New NNP work_53xuaunsqfhv7cuuzotagythj4 162 22 York York NNP work_53xuaunsqfhv7cuuzotagythj4 162 23 , , , work_53xuaunsqfhv7cuuzotagythj4 162 24 2008 2008 CD work_53xuaunsqfhv7cuuzotagythj4 162 25 . . . work_53xuaunsqfhv7cuuzotagythj4 163 1 [ [ -LRB- work_53xuaunsqfhv7cuuzotagythj4 163 2 23 23 CD work_53xuaunsqfhv7cuuzotagythj4 163 3 ] ] -RRB- work_53xuaunsqfhv7cuuzotagythj4 163 4 Wikipedia wikipedia NN work_53xuaunsqfhv7cuuzotagythj4 163 5 contributors contributor NNS work_53xuaunsqfhv7cuuzotagythj4 163 6 , , , work_53xuaunsqfhv7cuuzotagythj4 163 7 Euclid Euclid NNP work_53xuaunsqfhv7cuuzotagythj4 163 8 - - HYPH work_53xuaunsqfhv7cuuzotagythj4 163 9 Wikipedia Wikipedia NNP work_53xuaunsqfhv7cuuzotagythj4 163 10 , , , work_53xuaunsqfhv7cuuzotagythj4 163 11 The the DT work_53xuaunsqfhv7cuuzotagythj4 163 12 Free Free NNP work_53xuaunsqfhv7cuuzotagythj4 163 13 Encyclopedia Encyclopedia NNP work_53xuaunsqfhv7cuuzotagythj4 163 14 . . . work_53xuaunsqfhv7cuuzotagythj4 164 1 Url Url NNP work_53xuaunsqfhv7cuuzotagythj4 164 2 = = NFP work_53xuaunsqfhv7cuuzotagythj4 164 3 " " `` work_53xuaunsqfhv7cuuzotagythj4 164 4 https://en.wikipedia.org/wiki/Euclid https://en.wikipedia.org/wiki/euclid NN work_53xuaunsqfhv7cuuzotagythj4 164 5 " " '' work_53xuaunsqfhv7cuuzotagythj4 164 6 . . . work_53xuaunsqfhv7cuuzotagythj4 165 1 Hamid Hamid NNP work_53xuaunsqfhv7cuuzotagythj4 165 2 Ghorbani Ghorbani NNP work_53xuaunsqfhv7cuuzotagythj4 165 3 Department Department NNP work_53xuaunsqfhv7cuuzotagythj4 165 4 of of IN work_53xuaunsqfhv7cuuzotagythj4 165 5 Statistics Statistics NNPS work_53xuaunsqfhv7cuuzotagythj4 165 6 , , , work_53xuaunsqfhv7cuuzotagythj4 165 7 University University NNP work_53xuaunsqfhv7cuuzotagythj4 165 8 of of IN work_53xuaunsqfhv7cuuzotagythj4 165 9 Kashan Kashan NNP work_53xuaunsqfhv7cuuzotagythj4 165 10 , , , work_53xuaunsqfhv7cuuzotagythj4 165 11 Kashan Kashan NNP work_53xuaunsqfhv7cuuzotagythj4 165 12 , , , work_53xuaunsqfhv7cuuzotagythj4 165 13 I. I. NNP work_53xuaunsqfhv7cuuzotagythj4 165 14 R. R. NNP work_53xuaunsqfhv7cuuzotagythj4 165 15 Iran Iran NNP work_53xuaunsqfhv7cuuzotagythj4 165 16 E E NNP work_53xuaunsqfhv7cuuzotagythj4 165 17 - - NN work_53xuaunsqfhv7cuuzotagythj4 165 18 mail mail NN work_53xuaunsqfhv7cuuzotagythj4 165 19 : : : work_53xuaunsqfhv7cuuzotagythj4 165 20 hamidghorbani@kashanu.ac.ir hamidghorbani@kashanu.ac.ir CD