## Graham Irwin: sacred geometry

In life we come across numbers and shapes everywhere – a single point; two points joined by a straight line; a circle; a triangle; a sphere; a pyramid. The relationships between numbers, and the complexity of shapes, can be utterly fascinating.

One of the several ways to calculate pi (π), the ratio of a circleâ€™s circumference to its diameter, is using the following series:

π = ^{4}/_{1} – ^{4}/_{3} + ^{4}/_{5} – ^{4}/_{7} + ^{4}/_{9} – ^{4}/_{11} + ^{4}/_{13} ... which approximates to 3.1415926.

Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... Each number is the sum of the previous two. The ratio of two consecutive Fibonacci numbers tends towards what is known as the golden ratio, phi (φ). The golden ratio can be calculated as φ = ^{(1+√5)}/_{2} and has an approximate value of 1.618034. Rectangles with sides 1 : 1.618034 are thought to be more pleasing to the eye and are used a lot in photography, art and design.

There is a relationship between π and φ which can be expressed in the equation φ = cos (^{π}/_{5}).