In
link, a
diameter of a
link is any straight line segment that passes through the center of the kreis and whose endpoints are on the circle. The diameters are the longest
link of the circle. The word "diameter" derives from
link διάμετρος (diametros), "diagonal of a circle", from δια- (dia-), "across, through" + μέτρον (metron), "a measure".
In Mehr 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 kreis have the same length, this being twice the
link.
For a
link 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. 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.
