High Quality Content by WIKIPEDIA articles! In geometry, a curve of constant width is a convex planar shape whose width, defined as the distance between two opposite parallel lines touching its boundary, is the same regardless of the direction of those two parallel lines. One defines the width of the curve in a given direction to be the perpendicular distance between the parallels perpendicular to that direction. More generally, any compact convex planar body D has one pair of parallel supporting lines in a given direction. A supporting line is a line that has at least one point in common with the boundary of D but no points in common with the interior of D. One defines the width of the body as before. If the width of D is the same in all directions, then one says that the body is of constant width and calls its boundary a curve of constant width, and the planar body itself is referred to as an orbiform.

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