Diameter

Not to be confused with Demeter.

In geometry, the diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the boundary of the circle. The diameters are the longest chords of the circle. The word "diameter" is derived from Greek διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure").

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, because all diameters of a circle have the same length, this being twice the radius.

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 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. See also Tangent lines to circles. For a set of scattered points in the plane, the diameter of the points is the same as the diameter of their convex hull.