- Other WWW pages on Fibonacci and his series

There is much on the Web still to explore if these pages have sparked your interest in the Fibonacci numbers, Phi and the Golden string. Here are some suggestions for you to explore. - Books and other Articles

Books for teachers and for the interested general reader. - Current research and speculations

Some links on the more speculative applications of Fibonacci and Phi, or work in progress, for your perusal. What do*you*think?

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Dawson Merrill's Fibonacci and Phi links page is really excellent. I highly recommend it!

ACCESS Indiana's K-12 Teaching and Learning Center has an excellent page Fibonacci, Golden section, Art and Music links that is worth checking out.

Prof. Robert Devaney of Boston University has found the Fibonacci numbers in the Mandelbrot set and it's all to do with those buds on the outside of the set!

The Fibonacci Quarterly is devoted solely to the Fibonacci numbers and their uses. See also the current volume and other books by the Fibonacci Association too.

The early issues of the Fibonacci Quarterly have some useful introductions to the Fibonacci numbers suitable to pre-university (and undergraduate) students and I highly recommend them. The Quarterly started in 1963 but you may need to hunt through some University and College on-line periodicals catalogues to see who holds current and back copies.

The contents of some recent back copies give you an idea of the kind of papers published which are increasingly now only accessible to professional mathematicians. The earlier volumes (1960s and 1970s) are very readable by anyone who has enjoyed the pages at this site.

The Eleventh International Conference on Fibonacci Numbers and their Applications was held Braunschweig, Germany in July 2004. The Tenth Conference was held in Flagstaff, Arizona, USA in 2002 and the proceedings are now available: list of papers and authors. Proceedings of the Ninth conference at Luzembourg (2000) will not be published, but Eighth at Rochester, New York State, USA (1998) are published as Applications of the Fibonacci Numbers, Volume 8 edited by F T Howard, Kluwer Press, 1999. The Proceedings of earlier conferences in this series are available as books:

Applications of Fibonacci Numbers, Volume 7 edited by Gerald E. Bergum, Andreas N. Philippou and Alwyn F. Horadam, Kluwer Press, 1998.

Applications of Fibonacci Numbers, Proceedings of the Sixth International Conference edited by G E Bergum and A N Phillipou, Kluwer Press, 1996.

Dr Math is for secondary schools (US: elementary school and high schools) where you can ask "Dr Math" questions. Search Dr Math's archives to find some answers to previously asked questions about the Fibonacci numbers or the Golden section.

Don Cohen, alias the Mathman has some interesting samples of his workbooks on the Web. His approach to maths I heartily agree with and recommend to you - letting people discover the beauty and fascination of maths for themselves. Do have a look at this site if you're an educator, student or just interested in more maths! [Thanks to Bud Weiss of New York City for this.]

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means the whole book is useful andThe primary source for all information on the Fibonacci Numbers, the golden section and related topics is The Fibonacci Quarterly published by The Fibonacci Association. In particular an Index of all article titles is useful for finding what has been published already on your topic of interest. It starts from Volume 1 in 1963 and includes the biennial International Fibonacci Conferences of which the Twelfth is being held in July 2006 in San Francisco.

indicates an article in a magazine or else a paper in a professional journal where mathematicians and scientists report their latest findings (which may only be available in a college or university library).

The journal has some excellent introductory articles in its earlier volumes, a first-class resource for teachers at all levels from primary school to post-graduate.

V E Hoggatt Jr

H E Huntley's, The Divine Proportion: A study in mathematical beauty, ISBN 0-486-22254-3 is a 1970 Dover reprint of an old classic.

New Visual Perspectives on Fibonacci Numbers by K Atanassova, V Atanassova, A Shannon and J Turner, World Scientific (Oct 2002) introduces the idea of two intertwined Fibonacci-type series (2-Fibonacci series), recurrence trees and Gray codes, and a new Fibonacci vector as well as John Turner's goldpoint geometry (well known from his papers and presentations at the International Fibonacci Conferences and printed volumes) and fractals and tilings. Have a look at the publisher's description and the chapter titles.

Ian Stewart's

The Penguin Dictionary of Curious and Interesting Numbers, by David Wells, Penguin press, (new edition 1998) is full of interesting facts about all sorts of individual numbers. See the entry under 1·6180339887... for more information about Phi and the FIbonacci numbers. This is an excellent book! (More information and you can order it online via the title-link.)

Garth Runion's The Golden Section Dale Seymours publications, 1990, is also an excellent introduction to applications and maths on the Golden section and is very popular especially as a source for classroom work. (More information and you can order it online via the title-link.)

Theoni Pappas, The Joy of Mathematics: Discovering Mathematics All Around You, World Wide Publishers, 1989, ISBN: 0 93317465 9.

J & F Gies,

**Martin Gardner's books** are always worth looking at.
He has covered different aspects of the Fibonacci numbers in several of his books in his own
enthusiastic and fascinating style:

Mathematical Circus, Mathematical Association of America, 1992 , chapter 13.A complete list of his books is available at this Think.com site, with separate links to each book at Amazon.com's on-line bookstore. All of Gardner's books are a treasure trove of fun for the layman and also the professional mathematician who wants some recreational maths. He writes with a clarity that I guarantee will get returning to his books again and again.Fibonacci and Lucas Numbers

More mathematical puzzles and diversions, Mathematical Association of America press, ISBN: 0 14013823 4, (revised edition 1997), chapter 8Phi: the Golden Ratio

Penrose Tiles to Trapdoor Ciphers, 1997, chapters 1 and 2 onPenrose Tilingsand also chapter 8Wythoff's Nim

This is very useful too.

**Puzzle books by Henry E Dudeney**

Amusements in Mathematics, Dover Press, 1958, 250 pages.Books by Trudi Garland:

Still in print thanks to Dover in a very sturdy paperback format at an incredibly inexpensive price. This is a wonderful collection that I find I often dip into. There are arithmetic puzzles, geometric puzzles, chessboard [uzzles, an excellent chapter on all kinds of mazes and solving them, magic squares, river crossing puzzles, and more, all with full soutions and often extra notes! Highly recommended!

536 Puzzles and Curious Problems is now out of print, but you may be able to pick up a second hand version by clicking on this link. It is another collection likeAmusements in Mathematics(above) but containing different puzzles arranged in sections: Arithmetical and Algebraic puzzles, Geometrical puzzles, Combinatorial and Topological puzzles, Game puzzles, Domino puzzles, match puzzles and "unclassified" puzzles. Full solutions and index. A real treasure.

The Canterbury Puzzles, Dover 2002, 256 pages. More puzzles (not in the previous books) the first section with some characters from Chaucer'sCanterbury Talesand other sections on the Monks of Riddlewell, the squire's Christmas party, the Professors puzzles and so on and all with full solutions of course!

Fascinating Fibonaccis by Trudi Hammel Garland.S. Vajda,

Trudy is a teacher in California and has some more information on her book. She also has published several posters, including one on the golden section suitable for a classroom or your study room wall.

You should also look at her other Fibonacci books too:

Fibonacci Fun: Fascinating Activities with Intriguing Numbers Trudi Hammel Garland - a book for teachers;

Math and Music: Harmonious Connectionsby Trudi Hammel Garland, Charity Vaughan Kahn and Katarina Stenstedt .

This is a wonderful book - now out of print - which is full of formulae on the Fibonacci numbers and Phi. Do try and find it in your local college or university library. It is well worth dipping in to if you are studying maths at age 16 or beyond!

On the theme of good books for teachers,
Math Curse by Jon Scieszka and Lane Smith, published by Viking in 1995,
is the story of Mrs Fibonacci and, of course,
mentions the Fibonacci series. It is getting good reviews as a
book for (US) grades 4 to 8.

M R Schroeder
Number Theory in Science and Communication, With
Applications in Cryptography, Springer-Verlag, 1990. ISBN 3540158006.
This is a fascinating collection of all sorts of applications of Number Theory
to many areas of science and technology. It has sections on the Fibonacci Numbers,
the Golden section and the Rabbit
sequence (also called the Golden String).

Fractals, Chaos and Power Laws, M Schroeder, W H Freeman publishers, 1991. This
is another fascinating book with much on self-similar sequences and patterns, Fibonacci
and Phi. I have found myself dipping into this book time and time again.
There is a chapter on the forbidden five-fold symmetry and its relation to
the Fibonacci rabbits. (More information and you can order it online via the title-link.)

S Hildebrandt and A Tromba's
The Parsimonious Universe - Shape and Form in the Natural World

How scientists and mathematicians have sought the laws of shape of natural forms.

Books available
through the Fibonacci Association:

The index to all volumes
of the Fibonacci Quarterly is very useful. Use Edit>Find... on your browser menu
to search the page.

Eric W. Weisstein's **World of Mathematics**
list of books on Fibonacci numbers .

Some earlier Proceedings of the
Third,
Fourth,
Fifth and
Sixth
International Conference on
*Fibonacci Numbers and Their Applications* are available as books.
The editor of each is A N Philippou.

The latest is the
Seventh
edited by Gerald E. Bergum, Andreas N. Philippou and Alwyn F. Horadam .

amazon.com and
amazon.co.uk
are on-line sources for ordering books recommended at this site.

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If you are in the UK, try: |

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John Harris of Canada has been working for over 30 years on some aspects of astronomy - in particular, a rejection of Bode's Law (an ad hoc scheme to explain the mean distances of the planets from the sun). His own research involves Phi to make sense of the statistics of orbits, and it involves Phi! Phi in fact turned out to be the solution to a quadratic equation (Section 3) necessary to determine a log-linear function for the planetary periods. He speculates about the history of this subject - what do you think? [John's pages need some familiarity with logarithms and log graphs as well as astronomical terms such as synodic period.]

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© 1996-2006 Dr Ron Knott

updated 14 June 2006