Every 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.