The golden section, or ratio, is often used in design. If we have two dimensions then they aresaid to be in the golden ration if the ratio of the smaller to the large is equal to the ratio of the larger to the sum of both of them. ^{1}

e.g.

If *a* and *b* are the length and width of a page then they are in the golden ration if

a:b = b:(a+b) |
---|

For the purposes of design this ratio is aproximately 1:1.61803 or very approximately 5:8

This ratio is embodied in a squence of numbers called the Fibonacci sequence. Fibonacci was a mathematician interested in mapping unchecked breeding. He found that without death populations whould grow in a spiral sequence as follows:

0, 1, 1, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, …

This sequence is formed by starting with 0, 1 and forming new numbers by adding the preceeding two in the squence.

There are two interesting things about this sequence

- As the sequence continues the ratio of the neighbouring pairs approaches the golden ration 3:8 = 1:1.6 … 144:233 = 1:1.61806 … 987:1597 = 1:1.61803 …

- This sequence occurs naturally in nature in the construction of things like sea shells, sun flowers etc. Even the human body is said to include golden ratios.

**Fibonacci numbers expressed in the structure of a nautilus shell. Simular proportions ocurr frequently in nature.**

Designers often use the golden ratio and fibonacci numbers in their designs, as they find the proportions balanced and pleasing to the eye.

- Penguin classics have for 50 years been published in the standard size of 111 x 180 mm, which embodies the golden ratio.
- Le Corbusier incorporated a fibonacci sequence into his architectural designs.

**The floorplan of Le Corbusier's Villa Savoye uses fibonacci numbers**

- Many graphic designers and artists use fibonacci numbers to structure the page layout.

**A web page set out according to the golden ratio** ^{2}

**Leonardo Da Vinci used the golden ration in his art** ^{2}