# Category: Constant width

Curve of constant width
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of
Body of constant brightness
In convex geometry, a body of constant brightness is a three-dimensional convex set all of whose two-dimensional projections have equal area. A sphere is a body of constant brightness, but others exis
Reuleaux triangle
A Reuleaux triangle [ʁœlo] is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular dis
Reuleaux polygon
In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical example, the Reuleaux triangle, which in turn,
Barbier's theorem
In geometry, Barbier's theorem states that every curve of constant width has perimeter π times its width, regardless of its precise shape. This theorem was first published by Joseph-Émile Barbier in 1
Blaschke–Lebesgue theorem
In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form that every curve of a given width has area at le
Surface of constant width
In geometry, a surface of constant width is a convex form whose width, measured by the distance between two opposite parallel planes touching its boundary, is the same regardless of the direction of t
Reuleaux tetrahedron
The Reuleaux tetrahedron is the intersection of four balls of radius s centered at the vertices of a regular tetrahedron with side length s. The spherical surface of the ball centered on each vertex p