THE CIRCLE

 

A circle is a simple shape of Euclydean Geometry that is the set of all points in a plane that are at a given distance from a given point, the center. The distance between any of the points and the centre is called the radius. It can also be defined as the locus of a point equidistant from a fixed point. 

A circle is a simple closed curve which divides the plane into two regions: an interior and an exterior.A circle may also be defined as a special ellipse in which the two foci are coincident and the ccentricity is 0, or the two-dimensional shape enclosing the most area per unit   perimeter, using calculus of variations.

 
As proved by Archimedes, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius,which comes to π multiplied by the radius squared.