0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More..
About Fibonacci himself
(
St Andrews University)
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
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Proceedings of the Ninth conference at Luzembourg (2000) will not be published, but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:
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.]0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More..
means the whole book is useful and
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 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 most recent,
Twelfth
was held in July 2006 in San Francisco and
the next is 7 - 11 July 2008 in Patras, Greece.
V E Hoggatt Jr
Fibonacci and Lucas Numbers published by
The Fibonacci Association,
1969 (Houghton Mifflin). A very good introduction to the Fibonacci and Lucas Numbers written
by a founder of the Fibonacci Quarterly.
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
Mathematical Recreations column on page 96 of the January 1995 (vol.272 no.1)
issue of Scientific American.
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, Leonard of Pisa & the New Mathematics of the
Middle Ages, Thos Cromwell, New York, 1969. F Gies is the author of the
entry on Fibonacci numbers in the
Encyclopaedia Brittanica.
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:
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.
Puzzle books by Henry E Dudeney
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!
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 and Lucas numbers, and the Golden Section: Theory
and Applications, S Vajda, Dover Press (2008).
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 .
|
| |
|
If you are in the UK, try: |
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More..
John Harris of Canada has been working for over 30 years on some aspects of astronomy - in particular, a rejection of Bode's Law (one explanation of why the mean distances of the planets from the sun are as they are). His own research into the statistics of orbits, and it involves Phi. 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.]
Here for instance is a good way to remember the approximate mean distances of each planet from the sun in terms in Astronomical Units (AUs). One AU is is the mean distance of the earth from the sun so other planet's distances are measured in terms of the earth's.
with thanks to Alanas for this data
Planet Mean distance F(n)/3 Mercury 0.4 1/3 = 0.33 Venus 0.7 2/3 = 0.67 Earth 1.0 3/3 = 1.0 Mars 1.5 5/3 = 1.7 Asteroids 2.8 8/3 = 2.7 Jupiter 5.0 13/3 = 4.3 - 21/3 = 7 Saturn 10 34/3 = 11 Uranus 20 55/3 = 18 Neptune 30 89/3 = 30 Pluto 40 144/3 = 48
More Applications of Fibonacci Numbers and Phi
|
Fibonacci Home Page
WHERE TO NOW? The is the last page of Links and References |
This is the last topic. |
© 1996-2008 Dr Ron Knott
