What is a circle?

After deciding to design a set of stamps for Royal Mail, based on the 2012 Olympics in london, through the 5 circles of London, I feel it is necessary to explore the definition of a circle.

'The circle has been known since before the beginning of recoreded history. It is the basis for the wheel, which then related inventions such as gears, makes much of modern civilization possible. In mathematics, the study of the circle has helped inspire the development of geometry and calculus. Early Science, particularly geometry and Astrology & Astronomy, was connected to the divine for most medieval scholars, and many believed that there was something intrinsically "divine" or "perfect" hat could be found in circles.'

This Image, take from the 13th Century manuscript, is a symbol of God creating the world, represented by the compass. Also note the circle around his head, portraying the idea of a halo.

Circles often arise in nature, an example below of a Tycho Crater.