Claim: Pi is the ratio of a circle's circumference to its radius squared.

In geometry , a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle . It can also be defined as the longest chord of the circle . Both definitions are also valid for the diameter of a sphere .   In more modern usage , the length of a diameter is also called the diameter . In this sense one speaks of the diameter rather than a diameter -LRB- which refers to the line itself -RRB- , because all diameters of a circle or sphere have the same length , this being twice the radius r.     For a convex shape in the plane , the diameter is defined to be the largest distance that can be formed between two opposite parallel lines tangent to its boundary , and the width is often defined to be the smallest such distance . Both quantities can be calculated efficiently using rotating calipers . For a curve of constant width such as the Reuleaux triangle , the width and diameter are the same because all such pairs of parallel tangent lines have the same distance .   For an ellipse , the standard terminology is different . A diameter of an ellipse is any chord passing through the center of the ellipse . For example , conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one of them is parallel to the other one . The longest diameter is called the major axis .   The word `` diameter '' is derived from Greek διάμετρος -LRB- diametros -RRB- , `` diameter of a circle '' , from διά -LRB- dia -RRB- , `` across , through '' and μέτρον -LRB- metron -RRB- , `` measure '' . It is often abbreviated DIA , dia , d , or ⌀ .