Editing Curve of constant width (section)

==Definitions==
Width, and constant width, are defined in terms of the [[supporting line]]s of curves; these are lines that touch a curve without crossing it.
Every [[compact set|compact]] curve in the plane has two supporting lines in any given direction, with the curve sandwiched between them. The [[Euclidean distance]] between these two lines is the ''width'' of the curve in that direction, and a curve has constant width if this distance is the same for all directions of lines. The width of a bounded [[convex set]] can be defined in the same way as for curves, by the distance between pairs of parallel lines that touch the set without crossing it, and a convex set is a body of constant width when this distance is nonzero and does not depend on the direction of the lines. Every body of constant width has a curve of constant width as its boundary, and every curve of constant width has a body of constant width as its [[convex hull]].{{r|gardner|rt}}

Another equivalent way to define the width of a compact curve or of a convex set is by looking at its [[orthogonal projection]] onto a line. In both cases, the projection is a [[line segment]], whose length equals the distance between support lines that are perpendicular to the line. So, a curve or a convex set has constant width when all of its orthogonal projections have the same length.{{r|gardner|rt}}