Fibonacci Numbers and the Golden Section

This is the Home page for Dr Ron Knott's multimedia web site on the Fibonacci numbers, the Golden section and the Golden string hosted by the Mathematics Department of the University of Surrey, UK.

The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next)

The golden section numbers are ±0·61803 39887... and ±1·61803 39887...

The golden string is 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ...
a sequence of 0s and 1s that is closely related to the Fibonacci numbers and the golden section.

There is a large amount of information at this site (more than 200 pages if it was printed), so if all you want is a quick introduction then the first link takes you to an introductory page on the Fibonacci numbers and where they appear in Nature.

The rest of this page is a brief introduction to all the web pages at this site on
Fibonacci Numbers the Golden Section and the Golden String
together with their many applications.

What's New? - the FIBLOG latest entry: 25 May 2006


Fibonacci Numbers and Golden sections in Nature

The Puzzling World of Fibonacci Numbers

A pair of pages with plenty of playful problems to perplex the professional and the part-time puzzler!

The Intriguing Mathematical World of Fibonacci and Phi

The golden section numbers are also written using the Greek letters Phi Phi and phi phi.

The Golden Section

The golden section number is closely connected with the Fibonacci series and has a value of (sqrt5 + 1)/2 or:

1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More.. Calculator


which we call Phi (note the capital P) on these pages. The other number also called the golden section is Phi-1 or 0·61803... with exactly the same decimal fraction part as Phi. This value we call phi (with a small p) here. Phi and phi have some interesting and unique properties such as 1/phi is the same as 1+phi=Phi.
The third of Simon Singh's Five Numbers programmes broadcast on 13 March 2002 on BBC Radio 4 was all about the Golden Ratio. It is an excellent introduction to the golden section. I spoke on it about the occurrence in nature of the golden section and also the Change Puzzle.
RadioHear the whole programme (14 minutes) using the free RealOne Player.

The Golden String

The golden string is also called the Infinite Fibonacci Word or the Fibonacci Rabbit sequence. There is another way to look at Fibonacci's Rabbits problem that gives an infinitely long sequence of 1s and 0s called the Golden String:-
1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 ...

This string is a closely related to the golden section and the Fibonacci numbers.

Fibonacci - the Man and His Times

More Applications of Fibonacci Numbers and Phi

Fibonacci and Phi in the Arts

Reference


Awards for this WWW site

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