Further sources of Information on Fibonacci Numbers and
the Golden Section
This is a page of WWW links to other sites on Fibonacci numbers and the Golden section in
general, together with a list of useful books and articles that are recommended for further
reading. Most links are now incorprated next to their application on Dr Ron Knott's Fibonacci webpages.
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.
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.]
More fascinating facts on Fibonacci numbers:
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.
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.
The Fibonacci Association has put online a number of free PDF versions of popular books they have produced:
see this list.
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.)
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:
Mathematical Circus, Mathematical Association of America, 1992 , chapter 13.
Fibonacci and Lucas Numbers
Penrose Tiles to Trapdoor Ciphers,
1997,
chapters 1 and 2 on Penrose Tilings and also chapter 8 Wythoff's Nim
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.
This list of
all the chapter titles in Gardner's mathematics books is very useful too.
Puzzle books by Henry E Dudeney
Amusements in Mathematics, Dover Press, 1958, 250 pages.
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 like
Amusements 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's Canterbury Tales and 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!
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.)
Some speculations about the Fibonacci numbers and some propositions about Phi -
not proved, just conjectures, but for your interest!
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.
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.]
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