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The Fibonacci Sequence

Introduction

The Fibonacci sequence is a delightful string of numbers that reoccur often in mathematics.  The numbers are such that each number is the sum of the two preceding numbers, beginning at 0. The Mathematical Association of America has put together this virtual special issue of articles to celebrate the Fibonacci sequence.

The articles and book chapters below are free-access via this page up until 31 August  2019.

The American Mathematical Monthly

Article TitleAuthor(s)Journal Title Year
The Mandelbrot Set, the Farey Tree, and the Fibonacci SequenceRobert L. DevaneyThe American Mathematical Monthly 1999
Random Approaches to Fibonacci IdentitiesArthur T. Benjamin, Gregory M. Levin, Karl Mahlburg, Jennifer J. QuinnThe American Mathematical Monthly 2000
“Fibonacci, Chebyshev, and Orthogonal Polynomials,”Dov Aharonov, Alan Beardon, and Kathy DriverThe American Mathematical Monthly2005
Quotients of Fibonacci NumbersStephan Ramon Garcia and Florian LucaThe American Mathematical Monthly2016
“Passing the Buck and Firing Fibonacci: Adventures with the Stochastic Abacus,” Bruce TorrenceThe American Mathematical Monthl2019

 

 Math Horizons

Article TitleAuthor (s)Journal TitleYear
DO THE MATH!: Fibonacci or Fairy Tale?Burkard Polster & Marty RossMath Horizons2015
A Dozen Questions About Fibonacci NumbersJames Tanton Math Horizons2005
From the Golden Ratio to Fibonacci Phyllotaxis SpiralsDavid BachmanMath Horizons2019
An Unanticipated Decimal ExpansionAllen SchwenkMath Horizons2012
Fibonacci's Triangle and other Abominations Doug Ensley Math Horizons2003

Mathematics Magazine

Article TitleAuthor(s)Journal TitleYear
Coin Flipping, Dynamical Systems, and the Fibonacci Numbers.Kennedy, Stephen F.; Stafford, Matthew WMathematics Magazine1994
The Fibonacci numbers—exposedKalman, Dan; Mena, RobertMathematics Magazine2003
The Fibonacci numbers—exposed more discretely. Benjamin, Arthur T.; Quinn, Jennifer J.Mathematics Magazine2003
Conway's subprime Fibonacci sequences. Guy, Richard K.; Khovanova, Tanya; Salazar, Julian Mathematics Magazine2014
Aphid sequences: turning Fibonacci numbers inside out. Erickson, Samuel; Goyt, Adam M.; Reiswig, JosiahMathematics Magazine2018

College Mathematics Journal  

Article Title Author(s)Journal Title Year
Cookie Monster Devours NaccisLeigh Marie Braswell & Tanya Khovanova The College Mathematics Journal2014
Recounting Fibonacci and Lucas IdentitiesArthur T. Benjamin & Jennifer J. Quinn The College Mathematics Journal1999
Fibonacci Powers and a Fascinating TriangleDale K. Hathaway & Stephen L. Brown The College Mathematics Journal1997
Harmonic Series Meets Fibonacci SequenceHongwei Chen & Chris Kennedy The College Mathematics Journal2012
Misconceptions about the Golden RatioGeorge Markowsky The College Mathematics Journal1992

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