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\u5f15\u8a00\u6765\u81ea\u4e8e\u672c\u4e66\uff1a\u300aMaster Fibonacci: The Man Who Changed Math<\/a>\u300b. <\/em><\/p>\n\n\n\n

PART 1: ORIGINS OF THE FIBONACCI SEQUENCE<\/h4>\n\n\n\n

I. Calculating in Medieval Europe<\/a><\/p>\n\n\n\n

II. Leonardo Pisano, a.k.a Fibonacci<\/a><\/p>\n\n\n\n

III. Liber Abaci<\/a><\/p>\n\n\n\n

IV. Fibonacci\u2019s Intellectual Legacy<\/a><\/p>\n\n\n\n

\u201cArabic numerals in Europe.\u201d Italia Medievale. Medieval Italian Cultural Association, 3 April 2015, http:\/\/www.italiamedievale.org\/portale\/numerazione-araba-in-europa\/?lang=en<\/a>. Accessed 23 July 2018.<\/p>\n\n\n\n

\u201cB\u00e9la Bart\u00f3k \u2013 The Golden Ratio in Music.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ ms\/Virtual-exhibitions\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Reception-of-Fibonacci-numbers-and-the- golden-ratio\/Bela-Bartok-the-golden-ratio-in-music<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

\u201cBiography of Leonardo of Pisa.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/ms\/Virtuelle- Ausstellungen\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Biographie-von-Leonardo-Pisano<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

\u201cCalculating with Fingers.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtual- exhibitions\/Fibonacci.-Un-ponte-sul- Mediterraneo\/Fibonacci-s-significance-for-the-present-day\/ Calculating-with-fingers<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Devlin, K. Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World<\/a>. Princeton University Press, 2017.<\/p>\n\n\n\n

Devlin, K. The Man of Numbers: Fibonacci\u2019s Arithmetic Revolution<\/a>. Walker Publishing Company, New York, 2011.<\/p>\n\n\n\n

The Editors of Encyclopaedia Britannica. \u201cPisa.\u201d Britannica.com. Encyclop\u00e6dia Britannica, Inc., 2018, https:\/\/ www.britannica.com\/place\/Pisa-Italy<\/a>, Accessed 27 July 2018.<\/p>\n\n\n\n

\u201cEducation in Europe \u2013 Medieval Education.\u201d Science Encyclopedia \u2013 Jrank. Net Industries, 2018, http:\/\/ science.jrank.org\/pages\/9077\/Education-in-Europe-Medieval-Education.html<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

\u201cFibonacci.\u201d Famous Scientists. famousscientists.org, 17 July 2018, www.famousscientists.org\/fibonacci- leonardo-of-pisa\/<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Fitzpatrick, Richard, \u201cEuclid\u2019s Elements of Geometry.\u201d utexas.edu. The University of Texas at Austin, 2008, http:\/\/farside.ph.utexas.edu\/Books\/Euclid\/Elements.pdf<\/a>, Accessed 29 July 2018.<\/p>\n\n\n\n

Gies, F. C. \u201cFibonacci Biography & Facts.\u201d Encyclopaedia Britannica. Encyclop\u00e6dia Britannica, Inc.,11 June 2018, https:\/\/www.britannica.com\/biography\/Fibonacci<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Horadam, A. F. \u201cEight Hundred Years Young.\u201d Vol 31, pp 123-134. The Australian Mathematics Teacher, 1975, Evansville.edu. 2018, http:\/\/faculty.evansville.edu\/ck6\/bstud\/fibo.html<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Knott, Ron. \u201cA Brief Biographical Sketch of Fibonacci, His Life, Times and Mathematical Achievements.\u201d Surrey.ac.uk. University of Surrey, 25 July 2005, http:\/\/personal.ee.surrey.ac.uk\/Personal\/R.Knott\/Fibonacci\/fibBio.html<\/a>. Accessed 25 July 2018.<\/p>\n\n\n\n

Livio, M. The Golden Ratio: The Story of Phi, the World\u2019s Most Astonishing Number<\/a>. Broadway Books, New York, 2002.<\/p>\n\n\n\n

McClenon, R. \u201cLeonardo of Pisa and His Liber Quadratorum.\u201d The American Mathematical Monthly, Official Journal of the Mathematical Association of America. Volume XXVI. Jan. 1919, https:\/\/archive.org\/details\/jstor-2974039<\/a>. Accessed July 2018.<\/p>\n\n\n\n

O\u2019Connor, J. J. and E. F. Robertson. \u201cLeonardo Pisano Fibonacci.\u201d MacTutor History of Mathematics Archive, School of Mathematics and Statistics University of St Andrews, Scotland, 1998, http:\/\/www.history.mcs.st-andrews.ac.uk\/Biographies\/Fibonacci.html. Accessed 20 July 2018.<\/p>\n\n\n\n

O\u2019Shea, Thomas. \u201cTypus Arithmeticae.\u201d Dr. Thomas O\u2019Shea. 2018. https:\/\/www.drthomasoshea.com\/typus-arithmeticae.html<\/a>. Accessed 21 July 2018. \u201cThe Rabbit Problem.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtuelle-Ausstellungen\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Bedeutung-Fibonaccis-fuer-die-Gegenwart\/ Kaninchenaufgabe<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Radford, L. \u201cReviews for Mathematics Education across Time and Place.\u201d Dr. Thomas O\u2019Shea. 2018, https:\/\/www.drthomasoshea.com\/reviews.html<\/a>, Accessed 21 July 2018.<\/p>\n\n\n\n

Roselaar, S. \u201cEconomic Networks and Cultural Change in the Antique Mediterranean.\u201d The Blue Web, 2018, http:\/\/bluenetworks2014.weebly.com\/antiquity.html<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Scotta, T. C. and P. Marketos. \u201cOn the Origin of the Fibonacci Sequence.\u201d History. MCS. 23 Mar. 2014, http:\/\/www-history.mcs.st-and.ac.uk\/~history\/Publications\/fibonacci.pdf<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Sesiano, Jacques (1997-07-31). \u201cAb\u016b K\u0101mil\u201d. Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Springer. pp. 4\u20135.<\/p>\n\n\n\n

Smith, David Eugene and Louis Charles Karpinski. \u201cThe Project Gutenberg EBook of the Hindu-Arabic Numerals.\u201d Gutenberg. Project Gutenberg, 14 Sept. 2007, https:\/\/www.gutenberg.org\/files\/22599\/22599-h\/22599-h.htm<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

\u201cThe Transition from Roman to Hindu-Arabic Numerals.\u201d The Blue Web. 6 June 2014, http:\/\/ bluenetworks2014.weebly.com\/the-transition-from-roman-to-hindu-arabic-numerals.html<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Citations from Master Fibonacci: The Man Who Changed Math<\/a>. <\/em><\/p>\n\n\n\n

PART 2: THE FIBONACCI SEQUENCE<\/h4>\n\n\n\n

I. Fibonacci Sequence<\/a><\/p>\n\n\n\n

II. The Golden Ratio<\/a><\/p>\n\n\n\n

III. Phi<\/a><\/p>\n\n\n\n

IV. Geometric Constructions Involving Phi<\/a><\/p>\n\n\n\n

V. Chart of Terms<\/a><\/p>\n\n\n\n

\u201cCalculating.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtual-exhibitions\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Fibonacci-s-significance-for-the-present-day\/Calculating-with-fingers<\/a>. Accessed 08 Aug 2018.<\/p>\n\n\n\n

\u201cDevelopment of Numeral Systems.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/ Virtual-exhibitions\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Fibonacci-s-significance-for-the-present-day\/ Development-of-numeral-systems<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Devlin, K. Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World<\/a>. Princeton University Press, 2017.<\/p>\n\n\n\n

Devlin, K. The Man of Numbers: Fibonacci\u2019s Arithmetic Revolution<\/a>. Walker Publishing Company, New York, 2011.<\/p>\n\n\n\n

\u201cDispute Between Abacists and Algorists.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/ms\/ Virtuelle-Ausstellungen\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Bedeutung-Fibonaccis-fuer-die-Gegenwart\/ Streit-zwischen-Abakisten-und-Algoristen<\/a>. Accessed 10 Aug 2018.<\/p>\n\n\n\n

Donnegan, James, M.D. \u201cA New Greek and English Lexicon: Principally on the Plan of the Greek and German Lexicon of Schneider, the Words Alphabetically Arranged.\u201d Hilliard, Gray, Boston, 1834, https:\/\/archive.org\/ details\/newgreekenglishl00donnuoft<\/a>. Accessed 23 July 2018.<\/p>\n\n\n\n

\u201cEducation in Europe \u2013 Medieval Education.\u201d Science Encyclopedia \u2013 Jrank. Net Industries, 2018, http:\/\/science.jrank.org\/pages\/9077\/Education-in-Europe-Medieval-Education.html<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Eppstein. \u201cICS 161: Design and Analysis of Algorithms Lecture notes for January 9, 1996.\u201d geeksforgeeks. UCI Donald Bren School of Information & Computer Sciences. https:\/\/www.ics.uci.edu\/~eppstein\/ 161\/960109.html<\/a>. Accessed 09 Aug 2018.<\/p>\n\n\n\n

\u201cEuclid.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtual-exhibitions\/Fibonacci.- Un-ponte-sul-Mediterraneo\/Reception-of-Fibonacci-numbers-and-the-golden-ratio\/Euclid-construction-of- the-golden-ratio<\/a>. Accessed 9 Aug 2018.<\/p>\n\n\n\n

\u201cFibonacci.\u201d Famous Scientists. famousscientists.org, 10 Sept 2018, www.famousscientists.org\/fibonacci-leonardo-of-pisa\/<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Gascue\u00f1a, Dory. \u201cFibonacci and the Golden Ratio: Divine Geometry?\u201d Open Mind. BBVA Group, 15 March 2017, https:\/\/www.bbvaopenmind.com\/en\/science\/mathematics\/fibonacci-and-the-golden-ratio-divine-geometry\/<\/a>. Accessed 06 August 2018.<\/p>\n\n\n\n

Ghusayni, Badih. \u201cFavorite mathematics topics from the 12th Century to the 21st Century.\u201d Academic Journal Academic Journal. International Journal of Mathematics & Computer Science. Vol. 13 Issue 1, p83-104. 22p. 2018, http:\/\/content.ebscohost.com\/ContentServer.asp? EbscoContent=dGJyMMTo50SeprE4v%2BvlOLCmr1Cep7JSsqe4S7KWxWXS&ContentCust omer=dGJyMPGqskm1r7ZJuePfgeyx9Yvf5ucA&T=P&P=AN&S=R&D=a9h&K=127054609. Accessed 3 August 2018.<\/p>\n\n\n\n

Horadam, A.F. \u201cBook Review: Leonardo Pisano (Fibonacci)\u2014The Book of Squares (an annotated translation into modern English)\u2014L.E. Sigler, Academic Press 1987.\u201d University of New England, Armidale, Australia 2351, p 382. https:\/\/www.fq.math.ca\/Scanned\/26-4\/review.pdf<\/a>. Accessed 13 Aug 2018.<\/p>\n\n\n\n

Horadam, A. F. \u201cEight Hundred Years Young.\u201d Vol 31, pp 123-134. The Australian Mathematics Teacher, 1975, Evansville.edu. 2018, http:\/\/faculty.evansville.edu\/ck6\/bstud\/fibo.html<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Knott, Ron. \u201cA Brief Biographical Sketch of Fibonacci, His Life, Times and Mathematical Achievements.\u201d Surrey.ac.uk. University of Surrey, 25 July 2005, http:\/\/personal.ee.surrey.ac.uk\/Personal\/R.Knott\/Fibonacci\/ fibBio.html<\/a>. Accessed 25 July 2018.<\/p>\n\n\n\n

Knott, Ron. \u201cDudeney\u2019s Cows.\u201d Surrey.ac.uk. University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom, 25 September 2016, http:\/\/www.maths.surrey.ac.uk\/hosted-sites\/R.Knott\/Fibonacci\/fibnat<\/a>. Accessed 08 August 2018.<\/p>\n\n\n\n

Levy, Joel. A Curious History of Mathematics: The (BIG) Ideas from Early Number Concepts to Chaos Theory<\/a>. Andre Deutsch, London, 2013. Lines, Malcolm E. Think of a Number<\/a>. Adam Hilger, New York, 1990.<\/p>\n\n\n\n

Livio, M. The Golden Ratio: The Story of Phi, the World\u2019s Most Astonishing Number<\/a>. Broadway Books, New York, 2002. McClenon, R. \u201cLeonardo of Pisa and His Liber Quadratorum.\u201d The American Mathematical Monthly. Official Journal of the Mathematical Association of America, Volume XXVI. Jan. 1919, https:\/\/archive.org\/details\/jstor-2974039<\/a>. Accessed 2 July 2018.<\/p>\n\n\n\n

Meisner, Gary. \u201cSpirals and the Golden Ratio.\u201d GoldenNumber.net. PhiPoint Solutions, LLC, 25 Aug 2012, https:\/\/www.goldennumber.net\/spirals\/<\/a>. Accessed 13 Aug 2018.<\/p>\n\n\n\n

O\u2019Connor, J. J. and E. F. Robertson. \u201cLeonardo Pisano Fibonacci.\u201d MacTutor History of Mathematics Archive, School of Mathematics and Statistics University of St Andrews, Scotland, 1998, http:\/\/www-history.mcs.st-andrews.ac.uk\/Biographies\/Fibonacci.html<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

O\u2019Shea, Thomas. \u201cTypus Arithmeticae.\u201d Dr. Thomas O\u2019Shea. 2018. https:\/\/www.drthomasoshea.com\/typus-arithmeticae.html<\/a>. Accessed 21 July 2018.<\/p>\n\n\n\n

\u201cPhi in Atomic Structure.\u201d Sacred Geometry. Drupal, 2018, http:\/\/www.sacredgeometry.es\/?q=en\/content\/phi-atomic-structure, Accessed 10 Aug 2018.<\/p>\n\n\n\n

\u201cThe Rabbit Problem.\u201d ETH Zurich. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtuelle- Ausstellungen\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Bedeutung-Fibonaccis-fuer-die-Gegenwart\/ Kaninchenaufgabe<\/a>. Accessed 20 July 2018.<\/p>\n\n\n\n

Radford, L. \u201cReviews for Mathematics Education across Time and Place.\u201d Dr. Thomas O\u2019Shea. 2018, https:\/\/www.drthomasoshea.com\/reviews.html<\/a>, Accessed 21 July 2018.<\/p>\n\n\n\n

Scotta, T. C. and P. Marketos. \u201cOn the Origin of the Fibonacci Sequence.\u201d History. MCS. 23 Mar. 2014, http:\/\/www-history.mcs.st-and.ac.uk\/~history\/Publications\/fibonacci.pdf<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Seewald, Nick. \u201cThe Myth of the Golden Ratio.\u201d Golden Ratio Myth. Weebly, 2010, https:\/\/ goldenratiomyth.weebly.com\/a-brief-history-of-phi.html<\/a>. Accessed 6 Aug 2018.<\/p>\n\n\n\n

Seife, Charles. Zero: The Biography of a Dangerous Idea<\/a>. Viking, 2000.<\/p>\n\n\n\n

Sesiano, Jacques (1997-07-31). \u201cAb\u016b K\u0101mil.\u201d Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer. pp. 4\u20135.<\/p>\n\n\n\n

Smith and Karpinski. \u201cThe Hindu-Arabic Numerals, Boston and London, 1911.\u201d Archibald, Euclid\u2019s Book on Divisions of Figures; with a Restoration based on Woepcke\u2019s Text and on the Practica Geometrice, of Leonardo Pisano. Cambridge, England, 1915.<\/p>\n\n\n\n

TallBloke. \u201cA Remarkable Discovery: All Solar System Periods Fit the Fibonacci Series and the Golden Ratio. Why Phi?\u201d TallBloke\u2019s Talkshop, 20 Feb 2013, https:\/\/tallbloke.wordpress.com\/2013\/02\/20\/a-remarkable- discovery-all-solar-system- periods-fit-the-fibonacci-series-and-the-golden-ratio-why-phi<\/a>. Accessed 07 Aug 2018.<\/p>\n\n\n\n

\u201cThe Transition from Roman to Hindu-Arabic Numerals\u201d The Blue Web. Bluenetworks2014, 6 June 2014, http:\/\/bluenetworks2014.weebly.com\/the-transition-from-roman-to-hindu-arabic-numerals.html<\/a>. Accessed 10 Aug 2018.<\/p>\n\n\n\n

Velasquez, Robert. \u201c5 Reasons Using The Fibonacci Sequence Makes You Better At Agile Development.\u201d eLearningIndustry. 7 Nov 2017, https:\/\/elearningindustry.com\/using-the-fibonacci-sequence-makes-better- agile-development-5-reasons<\/a>. Accessed 13 Aug 2018.<\/p>\n\n\n\n

Watkins, John J. Number Theory: A Historical Approach<\/a>. Princeton University Press, 2013.<\/p>\n\n\n\n

Wolchover, Natalie. \u201cStrange Stars Pulse to the Golden Mean.\u201d Quanta Magazine. Quanta, 10 Mar 2015, https:\/\/www.quantamagazine.org\/variable-stars-have-strange-nonchaotic-attractors-20150310\/<\/a>. Accessed10 Aug 2018.<\/p>\n\n\n\n

PART 3: FIBONACCI IN ART & MUSIC<\/h4>\n\n\n\n

I. Fibonacci in Art & Architecture<\/a>
II. Fibonacci in Music<\/a>
III. Fibonacci in Film<\/a>
IV. Fibonacci in Applied Arts<\/a>
V. Disputation of Fibonacci in Art<\/a><\/p>\n\n\n\n

Akhtaruzzaman, Md. and Amir A. Shafie. \u201cGeometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering,\u201d International Journal of Arts, Vol. 1 No. 1, 2011, pp. 1-22. doi: 10.5923\/j.arts.20110101.01.<\/p>\n\n\n\n

Armienti, Pietro. \u201cThe Medieval Roots of Modern Scientific Thought. A Fibonacci Abacus in the Facade of the Church of San Nicola in Pisa Ietro.\u201d 2015, Journal of Cultural Heritage (2015), http:\/\/dx.doi.org\/10.1016\/j.culher.2015.07.015<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

\u201cAs Easy as 1, 1, 2, 3 \u2026.\u201d The Guardian. Guardian News and Media Limited, 12 May 2005, https:\/\/ www.theguardian.com\/music\/2005\/may\/12\/classicalmusicandopera1<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

Beer, M., 2008. \u201cMathematics and Music: Relating Science to Arts?\u201d Mathematical Spectrum, 41(1):36-42.  https:\/\/www.michael.beer.name\/File+download\/1\/mathandmusic.pdf<\/a> Accessed 20 Aug 2018.<\/p>\n\n\n\n

Bidwell, Eugene Boyd. \u201cViolin Design Method of Stradivari.\u201d Violincad.com. 2018, http:\/\/ www.violincad.com\/violin\/betts\/article.htm<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Birkhead, Mike. \u201cTips from a Combat Designer: Fibonacci Game Design.\u201d Gamasutra.com. UBM, 15 Feb 2012, https:\/\/www.gamasutra.com\/view\/news\/129642\/ Tips_from_a_combat_designer_Fibonacci_game_design.php<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Brandon, James. \u201cDivine Composition with Fibonacci\u2019s Ratio (The Rule of Thirds on Steroids).\u201d Digital Photography School. Digital Photography School, 2018, https:\/\/digital-photography-school.com\/divine- composition-with-fibonaccis-ratio-the-rule-of-thirds-on-steroids\/<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Cartwright, Mark. \u201cVitruvius.\u201d Ancient History Encyclopedia. Ancient History Encyclopedia Limited, 22 April 2015, https:\/\/www.ancient.eu\/Vitruvius\/<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Cohen, J. -L. (2014). Le Corbusier\u2019s Modulor and the Debate on Proportion in France. Architectural Histories, 2(1), Art. 23. DOI: http:\/\/doi.org\/10.5334\/ah.by<\/a>, https:\/\/journal.eahn.org\/articles\/10.5334\/ah.by\/<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

Du Sautoy, Marcus. \u201cListen by Numbers: Music and Maths.\u201d The Guardian. Guardian News, 27 Jun 2011, https:\/\/www.theguardian.com\/music\/2011\/jun\/27\/music-mathematics-fibonacci<\/a>. Accessed 18 Aug 2018.<\/p>\n\n\n\n

Edmark, John. \u201cJohn Edmark\/Work\/Golden Angle.\u201d John Edmark. John Edmark, 2018, http:\/\/ www.johnedmark.com\/work\/golden-angle\/. Accessed 22 Aug 2018.<\/p>\n\n\n\n

\u201cThe Fibonacci Numbers Have Been Discovered on a Church in Pisa.\u201d 18 Sep 2015, https:\/\/sandrozicari.com\/ 2015\/09\/18\/the-fibonacci-numbers-have-been-discovered-on-a-church-in-pisa\/<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

\u201cFibonacci \u2013 The Flight of the Numbers.\u201d Arte.it. ART.it, 23 Aug 2018. http:\/\/www.arte.it\/work_of_art\/ fibonacci-the-flight-of-the-numbers-5739<\/a>. Accessed 23 Aug 2018.<\/p>\n\n\n\n

Fischler, Roger. \u201cOn the Application of the Golden Ratio in the Visual Arts.\u201d Leonardo, vol. 14, no. 1, 1981, pp. 31\u201332. JSTOR, JSTOR, www.jstor.org\/stable\/1574475<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Frampton, Hollis, and Scott MacDonald. \u201cInterview with Hollis Frampton: The Early Years.\u201d October, vol. 12, 1980, pp. 103\u2013126. JSTOR, JSTOR, www.jstor.org\/stable\/778577<\/a>. Accessed 20 Aug. 2018.<\/p>\n\n\n\n

Grandinetti, Mary-Jane. \u201cThe Fib Review.\u201d Muse-Pie Press. 30 Jun 2018, http:\/\/www.musepiepress.com\/ fibreview\/index.html<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Haylock, Derek. \u201cGolden Ratio and Beethoven\u2019s 5th.\u201d Derek-Haylock.blogspot.com http:\/\/derek-haylock.blogspot.com\/2014\/08\/golden-ratio-and-beethovens-5th.html<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Hoijer, Natalie. \u201cUnleashing Music\u2019s Hidden Blueprint: An Analysis of Mathematical Symmetries Used in Music.\u201d IWU.edu, Digital Commons @ Illinois Wesleyan University. 2015, https:\/\/digitalcommons.iwu.edu\/ cgi\/viewcontent.cgi?article=1007&context=music_papers<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Hom, Elaine J. \u201cWhat Is the Golden Ratio?\u201d LiveScience.com. Purch, 24 Jun 2013, https:\/\/ www.livescience.com\/37704-phi-golden-ratio.html. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Horadam, A. F. \u201cEight Hundred Years Young.\u201d Vol 31, pp 123-134. The Australian Mathematics Teacher, 1975, Evansville.edu. 2018, http:\/\/faculty.evansville.edu\/ck6\/bstud\/fibo.html<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

\u201cHow We Built the Core.\u201d Eden Project.com. Eden Project, https:\/\/www.edenproject.com\/eden-story\/behind- the-scenes\/how-we-built-the-core<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Hunt, Patrick. \u201cMozart and Mathematics.\u201d Electrum Magazine. Electrum Magazine, 30 June 2013, http:\/\/ www.electrummagazine.com\/2013\/06\/mozart-and-mathematics\/<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Iyer, Vijay. \u201cStrength in Numbers: How Fibonacci Taught Us How to Swing.\u201d The Guardian. Guardian News and Media Limited, 15 Oct 2009, https:\/\/www.theguardian.com\/music\/2009\/oct\/15\/fibonacci-golden-ratio<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

\u201cJourney to the Core.\u201d Eden Project.com. Eden Project, 2018, https:\/\/www.edenproject.com\/sites\/default\/ files\/documents\/journey-to-the-core.pdf<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Klykavka, Oleksandr. \u201cSolar Observatory in Ukraine.\u201d Ancient History Et Cetera. Ancient History et cetera, 15 Dec 2016, http:\/\/etc.ancient.eu\/education\/solar-observatory-ukraine\/<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

\u201cLe Corbusier \u2013 the Modulor.\u201d ETH Library. ETH Library, 2018, http:\/\/www.library.ethz.ch\/en\/ms\/Virtual- exhibitions\/Fibonacci.-Un-ponte-sul-Mediterraneo\/Reception-of-Fibonacci-numbers-and-the-golden-ratio\/Le- Corbusier-the-Modulor<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

Livio, Mario. The Golden Ratio: The Story of PHI, the World\u2019s Most Astonishing Number<\/a>. Broadway Books; Reprint edition, 2003.<\/p>\n\n\n\n

Lobo, Carmen. \u201cFibonacci Met Reinfried Marass, but Who is Fibonacci?\u201d ART & Thoughts. ART & Thoughts, 10 Feb 2013, https:\/\/articulosparapensar.wordpress.com\/2013\/02\/10\/fibonacci-met-reinfried- marass-but-who-is-fibonacci\/<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

McNally, Jess. \u201cEarth\u2019s Most Stunning Natural Fractal Patterns.\u201d Wired.com. Conde Nast, 9 Oct 2010, https:\/\/www.wired.com\/2010\/09\/fractal-patterns-in-nature\/<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

Meisner, Gary. \u201cAcoustics and the Golden Ratio.\u201d Golden Number.net. PhiPoint Solutions, LLC, 2018, https:\/\/ www.goldennumber.net\/acoustics\/<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Miller, Peter H. \u201cThe Neuroscience of Traditional Architecture: Looking at Architectural Ornament Soothes Our Senses and Lifts Our Spirits.\u201d Traditional Building.com. Active Interest Media, 10 May 2018, https:\/\/ www.traditionalbuilding.com\/opinions\/neuroscience-architecture<\/a>. Accessed 18 Aug 2018.<\/p>\n\n\n\n

Paphides, Pete. \u201cThe Music of Mathematics.\u201d Times, the (United Kingdom), n.d. https:\/\/www.thetimes.co.uk\/ article\/delia-derbyshire-the-music-of-mathematics-mjbt5ts6g5z<\/a>. Accessed 18 Aug 2018.<\/p>\n\n\n\n

Parkin, Simon. \u201cThe Video Game that Maps the Galaxy.\u201d The New Yorker. Conde Nast, 9 Jul 2014, https:\/\/ www.newyorker.com\/tech\/elements\/the-video-game-that-maps-the-galaxy<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Pascoe, Clive B. \u201cMotivational Pacing in Musical Design an Active Force in Music Education.\u201d Contributions to Music Education, no. 3, 1974, pp. 106\u2013112. JSTOR, JSTOR, www.jstor.org\/stable\/24126929<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Pincus, Greg. \u201cGreg Pincus \u2013 Writer Guy.\u201d Greg Pincus. Greg Pincus, 2013, http:\/\/www.gregpincus.com\/ the-14-fibs.html<\/a>. Accessed 24 Aug 2018.<\/p>\n\n\n\n

Posamentier, Alfred S. and Ingmar Lehmann. The (Fabulous) Fibonacci Numbers. Prometheus Books, NY, 2007. Rogers, Michael R. \u201cChopin, Prelude in A Minor, Op. 28, No. 2.\u201d 19th-Century Music, vol. 4, no. 3, 1981, pp. 245\u2013250. JSTOR, JSTOR, www.jstor.org\/stable\/746697<\/a>. Accessed 20 Aug 2018.<\/p>\n\n\n\n

Rory PQ, \u201cMusic and the Fibonacci Sequence w\/ Rory PQ.\u201d Dubspot. DS14, Inc. \u2013 Dubspot. 1 Jun 2016. http:\/\/blog.dubspot.com\/fibonacci-sequence-in-music\/<\/a> Accessed 29 Oct 2018.<\/p>\n\n\n\n

Salingaros, Nikos A. Applications of the Golden Mean to Architecture in Meandering through Mathematics, 2012.<\/p>\n\n\n\n

Salingaros, Nikos A. Why Monotonous Repetition is Unsatisfying in Meandering through Mathematics, 2011.<\/p>\n\n\n\n

Sartwell, Crispin, \u201cBeauty\u201d, The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.), https:\/\/plato.stanford.edu\/archives\/win2017\/entries\/beauty\/<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Shamsian, Jacob and Carl Mueller. \u201cAn Artist Uses Mathematical Formulas to Make Otherworldly Geometric Sculptures.\u201d Business Insider. Insider Inc. https:\/\/www.businessinsider.com\/artist-john-edmark-uses-math- to-make-otherworldly-geometric-sculptures-2016-4?r=US&IR=T&IR=T<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Sinha, Sudipta. \u201cThe Fibonacci Numbers and Its Amazing Applications.\u201d International Journal of Engineering Science Invention ISSN (Online): 2319 \u2013 6734, ISSN (Print): 2319 \u2013 6726 www.ijesi.org ||Volume 6 Issue 9|| September 2017 || PP. 07-14, http:\/\/www.ijesi.org\/papers\/Vol(6)9\/Version-3\/B0609030714.pdf<\/a>. Accessed 22 Aug 2018.<\/p>\n\n\n\n

Spinak, Mike. The Golden Section Hypothesis: A Critical Look in Naturography. 2011.<\/p>\n\n\n\n

Stakhov, Alexey. \u201cThe Mathematics of Harmony: Euclid to Contemporary Mathematics and Computer Science.\u201d World Scientific.com. World Scientific Publishing Co. Pte. Ltd., 2018, http:\/\/ www.worldscibooks.com\/mathematics\/6635.html. Accessed 23 Aug 2018.<\/p>\n\n\n\n

Stefanovic, Konstantin. \u201cDynamic Symmetry and Golden Section.\u201d Eng trans: Ana Smiljanic. Sanu.ac. n.d. http:\/\/www.mi.sanu.ac.rs\/vismath\/jadrbookhtml\/part42.html<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Sylvestre, Lo\u00efc, and Marco Costa. \u201cThe Mathematical Architecture of Bach\u2019s \u2018The Art of Fugue.\u2019\u201d Il Saggiatore Musicale, vol. 17, no. 2, 2010, pp. 175\u2013195. JSTOR, JSTOR, www.jstor.org\/stable\/43030058<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Van Gend, Robert. \u201cThe Fibonacci Sequence and the Golden Ratio in Music.\u201d Notes on Number Theory and Discrete Mathematics ISSN 1310\u20135132 Vol. 20, 2014, No. 1, 72\u201377, http:\/\/www.nntdm.net\/papers\/ nntdm-20\/NNTDM-20-1-72-77.pdf<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Weisstein, Eric W. \u201cGolden Spiral.\u201d MathWorld. A Wolfram Web Resource. 31 Jul 2018, http:\/\/ mathworld.wolfram.com\/GoldenSpiral.html<\/a>. Accessed 21 Aug 2018.<\/p>\n\n\n\n

Wu, Feng. \u201cStradivarius: Music of the Golden Ratio.\u201d WufengEngineering. WordPress, 18 Jan 2015, https:\/\/ wufengengineering.wordpress.com\/2015\/01\/18\/stradivarius-music-of-the-golden-ratio\/. Accessed 21 Aug 2018.<\/p>\n\n\n\n

PART 4: FIBONACCI IN NATURE<\/h4>\n\n\n\n

I. Fibonacci in Nature<\/a>
II. Fibonacci and Insects<\/a>
III. Fibonacci and Animals<\/a>
IV. Fibonacci in Space & Geography<\/a>
V. Fibonacci in Humans<\/a><\/p>\n\n\n\n

Akhtaruzzaman, Md. and Amir A. Shafie. \u201cGeometrical Substantiation of Phi, the Golden Ratio and the Baroque of Nature, Architecture, Design and Engineering.\u201d International Journal of Arts p-ISSN: 2168-4995 e-ISSN: 2168-5002. 2011. 1(1): 1-22. doi: 10.5923\/j.arts.20110101.01. Scientific & Academic Publishing. 2012, http:\/\/article.sapub.org\/10.5923.j.arts.20110101.01.html<\/a>. Accessed 19 Aug 2018.<\/p>\n\n\n\n

Ashrafian H, Athanasiou T. \u201cFibonacci Series and Coronary Anatomy.\u201d Heart Lung Circ 2011 Jul;20(7):483\u20134.<\/p>\n\n\n\n

Bellos, Alex. \u201cGolden ratio discovered in uterus.\u201d The Guardian. Guardian News and Media Limited, 14 Aug 2012. https:\/\/www.theguardian.com\/science\/alexs-adventures-in-numberland\/2012\/aug\/14\/ golden-ratio- uterus<\/a>. Accessed 06 Sep 2018.<\/p>\n\n\n\n

Britton, Jill. \u201cFibonacci Numbers in Nature.\u201d 20 Jun 2011. https:\/\/archive.li\/t2RY<\/a> http:\/\/ britton.disted.camosun.bc.ca\/fibslide\/jbfibslide.htm. Accessed 29 Aug 2018.<\/p>\n\n\n\n

Boeyens JCA, Thackeray JF. \u201cNumber Theory and the Unity of Science.\u201d S Afr J Sci. 2014;110(11\/12), Art. #a0084, 2 pages. http:\/\/dx.doi. org\/10.1590\/sajs.2014\/a0084<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Cartwright, Jon. \u201cFibonacci Spirals in Nature Could Be Stress-Related.\u201d SOTT.net: Signs of the Times. PhysicsWeb. 26 Apr 2007 07:13 UTC, https:\/\/sott.net\/en130945<\/a>, Accessed 1 Sep 2018.<\/p>\n\n\n\n

Chin, Gilbert J. \u201cOrganismal Biology: Flying Along a Logarithmic Spiral.\u201d Science, 290 (5498): 1857, 8 Dec 2000, doi:10.1126\/science.290.5498.1857c Coxeter, H. S. M. Introduction to Geometry. Wiley: New York, 1961, p. 172.<\/p>\n\n\n\n

D\u2019Agnese, Joseph Blockhead: The Life of Fibonacci<\/a>. Henry Holt and Co. (BYR); First edition. 30 Mar 2010, p. 40.<\/p>\n\n\n\n

Davis, T. Antony. \u201cWhy Fibonacci Sequence for Palm Leaf Spirals?.\u201d (1971), http:\/\/library.isical.ac.in:8080\/ jspui\/bitstream\/10263\/897\/1\/TFQ-9-3-1971- P237-244.pdf<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Devlin, K. The Man of Numbers: Fibonacci\u2019s Arithmetic Revolution<\/a>. Walker Publishing Company, New York, 2011.<\/p>\n\n\n\n

Farina, A & Fantacci, Claudio & Frasca, Marco. (2014). \u201cStochastic Filtering of a Random Fibonacci Sequence: Theory and Applications. Signal Processing. 104. 212\u2013224. 10.1016\/j.sigpro.2014.03.052. https:\/\/ www.researchgate.net\/publication\/ 262193339_Stochastic_filtering_of_a_random_Fibonacci_sequence_Theory_and_applications Accessed 04 Sep 2018.<\/p>\n\n\n\n

Gibson CM, Gibson WJ, Murphy SA, Marble SJ, McCabe CH, Turakhia MP, et al. \u201cAssociation of the Fibonacci Cascade with the Distribution of Coronary Artery Lesions Responsible for ST-Segment Elevation Myocardial Infarction.\u201d Am J Cardiol 2003;92(5):595\u20137.<\/p>\n\n\n\n

Green, Christopher D. \u201cAll That Glitters: a Review of Psychological Research on the Aesthetics of the Golden Section.\u201d Perception. volume 24, 20 Mar 1995, 937-968 Department of Psychology, York University, North York, Ontario M3J 1P3, Canada.<\/p>\n\n\n\n

Green, Christopher D. \u201cMathematical and Historical Background to \u2018All That Glitters\u2026: A Review of Psychological Research on the Aesthetics of the Golden Section\u2019.\u201d Department of Psychology, York University, North York, Ontario M3J 1P3 CANADA. http:\/\/www.yorku.ca\/christo\/papers\/goldhist.htm<\/a> Accessed 04 Sep 2018.<\/p>\n\n\n\n

Horadam, A. F. \u201cEight Hundred Years Young.\u201d Vol 31, pp 123-134. The Australian Mathematics Teacher, 1975, Evansville.edu. 2018, http:\/\/faculty.evansville.edu\/ck6\/bstud\/fibo.html<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Hutchison A. L. and R. L. Hutchison. \u201cFibonacci, Littler, and the Hand: a Brief Review.\u201d Hand 2010;5:364\u20138. Iosa, Marco; Fusco, Augusto; and Fabio Marchetti, et al., \u201cThe Golden Ratio of Gait Harmony: Repetitive Proportions of Repetitive Gait Phases,\u201d BioMed Research International, vol. 2013, Article ID 918642, 7 pages, 2013. https:\/\/doi.org\/10.1155\/2013\/918642<\/a>. Accessed 06 Sep 2018.<\/p>\n\n\n\n

Iosa, Marco; Morone, Giovanni; and Stefano Paolucci. \u201cGolden Gait: An Optimization Theory Perspective on Human and Humanoid Walking.\u201d Frontiers in Neurorobotics. 19 Dec 2017, https:\/\/www.frontiersin.org\/ articles\/10.3389\/fnbot.2017.00069\/full<\/a>. Accessed 09 Sep 2018.<\/p>\n\n\n\n

Jefferson, Yosh, DMD. \u201cFacial Beauty \u2013 Establishing a Universal Standard.\u201d IJO. Vol 15, No 1, 2004, http:\/\/ facialbeauty.org\/article\/FacialBeauty.pdf<\/a>. Accessed 09 Sep 2018.<\/p>\n\n\n\n

Junod, Tom. \u201cThe Falling Man.\u201d Esquire. Hearst Communications, Inc. 9 Sep 2016, https:\/\/ www.esquire.com\/news-politics\/a48031\/the-falling-man-tom-junod<\/a>\/. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Kawakami S, Tsukada S, Hayashi H, Takada Y, Koubayashi S. \u201cGolden Proportion for Maxillofacial Surgery in Orientals.\u201d Annals of Plastic Surgery. 1989 Nov; 23(5) 417-425. PMID: 2604329. https:\/\/europepmc.org\/ abstract\/med\/2604329<\/a>. Accessed 09 Sep 2018.<\/p>\n\n\n\n

Knott, Ron. \u201cA Brief Biographical Sketch of Fibonacci, His Life, Times and Mathematical Achievements.\u201d Surrey.ac.uk. University of Surrey, 25 July 2005, http:\/\/personal.ee.surrey.ac.uk\/Personal\/R.Knott\/Fibonacci\/ fibBio.html<\/a>. Accessed 25 July 2018.<\/p>\n\n\n\n

Leppik, Elmar E. \u201cEvolutionary Differentiation of the Flower Head of the Compositae II.\u201d Annales Botanici Fennici, vol. 7, no. 4, 1970, pp. 325\u2013352. JSTOR, JSTOR, www.jstor.org\/stable\/23724678<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Littler JW. \u201cOn the Adaptability of Man\u2019s Hand (with Reference to the Equiangular Curve).\u201d Hand 1973;5(3): 187\u201391.<\/p>\n\n\n\n

\u201cLive Algae Specimens.\u201d Niles Bio.com. Niles Biological, Inc. 7 Sep 2018, http:\/\/www.nilesbio.com\/ subcat103.html<\/a>. Accessed 07 Sep 2018.<\/p>\n\n\n\n

Livio, Mario. \u201cThe Golden Number.\u201d Natural History, vol. 112, no. 2, 03, 2003, pp. 64-69. ProQuest, https:\/\/ search.proquest.com\/docview\/210617375?accountid=7494<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Majumder PP and Chakravarti A. \u201cVariation in the Number of Ray- and Disk- Florets in Four Species of Compositae.\u201d Fibonacci Q. 14, 97\u2013100. 1976, Google Scholar, https:\/\/www.fq.math.ca\/Scanned\/14-2\/ majumder.pdf<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Marco, Iosa and Morone Giovanni, Paolucci Stefano. \u201cGolden Gait: An Optimization Theory Perspective on Human and Humanoid Walking.\u201d Frontiers in Neurorobotics Vol 11, 2017. https:\/\/www.frontiersin.org\/ article\/10.3389\/fnbot.2017.00069<\/a>. DOI=10.3389\/fnbot.2017.00069. Accessed 06 Sep 2018.<\/p>\n\n\n\n

Masran, Mohd Rezuan. \u201cFibonacci Sequence and Orderliness as Observed in the Creations of Allah.\u201d Abstract. ONLINE JOURNAL OF RESEARCH IN ISLAMIC STUDIES 1.1 (2014): 104-122. https:\/\/works.bepress.com\/ rezuan\/1\/<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Meisner, Gary. \u201cGolden Ratio Overview.\u201d GoldenNumber.net. PhiPoint Solutions, LLC, 12 Jul 2015, https:\/\/ www.goldennumber.net\/golden-ratio\/<\/a>. Accessed 08 Sep 2018.<\/p>\n\n\n\n

Okabe, Takuya. \u201cPhysical Phenomenology of Phyllotaxis.\u201d Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432-8561, Japan, arXiv:1011.1981 [physics.bio-ph]. https:\/\/arxiv.org\/pdf\/1011.1981v3.pdf<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

\u201cThe Plant List: Compositae\u201d. Royal Botanic Gardens Kew and Missouri Botanic Garden. The Plant List (2013). Version 1.1. Published on the Internet; http:\/\/www.theplantlist.org\/<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Sacco, R.G. \u201cFibonacci Harmonics: A New Mathematical Model of Synchronicity.\u201d Applied Mathematics, 9, 702-718. https:\/\/doi.org\/10.4236\/am.2018.96048<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Scotta, T. C. and P. Marketos. \u201cOn the Origin of the Fibonacci Sequence.\u201d History. MCS. 23 Mar. 2014, http:\/\/ www-history.mcs.st-and.ac.uk\/~history\/Publications\/fibonacci.pdf<\/a>. Accessed 19 July 2018.<\/p>\n\n\n\n

Seewald, Nick. \u201cPhyllotaxis: The Fibonacci Sequence in Nature.\u201d Golden Ratio Myth. Weebly, 2010, https:\/\/ goldenratiomyth.weebly.com\/phyllotaxis-the-fibonacci-sequence-in-nature.html<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Shabalkin, I.P., Grigor\u2019eva, E. Yu., Gudkova, M.V., and Shabalkin, P.I. \u201cFibonacci Sequence and Supramolecular Structure of DNA.\u201d 20 May 2014. Translated from Kletochnye Tekhnologii v Biologii i Meditsine, No. 1, pp. 60-64, January, 2016, https:\/\/search.proquest.com\/docview\/1860892882\/C12EB9450A12478APQ\/1? accountid=7494<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Sinha, Sudipta. \u201cThe Fibonacci Numbers and Its Amazing Applications.\u201d International Journal of Engineering Science Invention ISSN (Online): 2319 \u2013 6734, ISSN (Print): 2319 \u2013 6726 www.ijesi.org ||Volume 6 Issue 9|| September 2017 || PP. 07-14, http:\/\/www.ijesi.org\/papers\/Vol(6)9\/Version-3\/B0609030714.pdf<\/a>. Accessed 06 Sep 2018.<\/p>\n\n\n\n

Spooner, David. The Poem and the Insect: Aspects of Twentieth Century Hispanic Culture<\/a>. UPA 19 Mar 2002. pp. 37-38.<\/p>\n\n\n\n

Swinton J, Ochu E. \u201cNovel Fibonacci and Non-Fibonacci Structure in the Sunflower: Results of a Citizen Science Experiment.\u201d MSI Turing\u2019s Sunflower Consortium. R Soc Open Sci. 2016 May; 3(5):160091. Epub 2016 May 18.<\/p>\n\n\n\n

National Center for Biotechnology Information, U.S. National Library of Medicine, 2018, https:\/\/www.ncbi.nlm.nih.gov\/pubmed\/27293788<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Tracy, Suzanne, and HPC Source. \u201cCelebrating Fibonacci Day 2015 on Monday, November 23.\u201d Scientific Computing, 2015. ProQuest, https:\/\/search.proquest.com\/docview\/1739102165?accountid=7494<\/a>. Accessed 05 Sep 2018.<\/p>\n\n\n\n

Trinajsti\u0107, Nenad. \u201cThe Magic of the Number Five.\u201d Croatica Chemica Acta 66.1 (1993): 227-254.<\/p>\n\n\n\n

Tung, K.K. Topics in Mathematical Modeling<\/a>. Princeton: Princeton University Press. 2007. Print.<\/p>\n\n\n\n

Verguts, J.; Ameye, L.; Bourne, T. and Timmerman, D. (2013), \u201cNormative Data for Uterine Size According to Age and Gravidity and Possible Role of the Classical Golden Ratio.\u201d Ultrasound Obstet Gynecol, 42: 713-717. doi:10.1002\/uog.12538<\/p>\n\n\n\n

Wright, Michael Lowe. \u201cThe Golden Mean.\u201d Vashti.net. Michael\u2019s Crazy Enterprises, Inc., 2017, http:\/\/ www.vashti.net\/mceinc<\/a>. Accessed 04 Sep 2018.<\/p>\n\n\n\n

Yetkin, G., Sivri, N., Yalta, K., and Yetkin, E. \u201cGolden Ratio is Beating in Our Heart.\u201d Int J Cardiol. 2013 Oct 12; 168(5):4926-7. http:\/\/dx.doi.org\/10.1016\/j.ijcard.2013.07.090<\/a>. Accessed 06 Sep 2018.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5f15\u8a00\u6765\u81ea\u4e8e\u672c\u4e66\uff1a\u300aMaster Fibonacci: The Man Who Changed Math\u300b.&n […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/pages\/145"}],"collection":[{"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/comments?post=145"}],"version-history":[{"count":2,"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/pages\/145\/revisions"}],"predecessor-version":[{"id":147,"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/pages\/145\/revisions\/147"}],"wp:attachment":[{"href":"https:\/\/www.fibonance.com\/index.php\/wp-json\/wp\/v2\/media?parent=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}