Reuleaux triangle

A Reuleaux triangle is a constant-width curve formed by three circular arcs centered at the vertices of an equilateral triangle. Its width is the same in every direction, despite its noncircular shape.

Constant-width curve: A plane curve whose distance between every pair of parallel supporting lines is the same. The Reuleaux triangle is a noncircular example of this broader geometric family.
Reuleaux triangle drill bit: A rotating tool shaped to trace an approximately square hole. A Reuleaux-triangle-like path lets a drill reach near-square corners.
Circle: The set of points in a plane at a fixed distance from a center. A circle has constant width too, but unlike the Reuleaux triangle it has a continuously curved boundary.
Franz Reuleaux: A German engineer known for systematic study of machine kinematics and mechanisms. The curve bears his name through his influence on the geometry of mechanical motion.
Equilateral triangle: A triangle with three equal sides and three equal angles. Its vertices locate the centers of the Reuleaux triangle’s three defining arcs.
Wankel engine: A rotary internal-combustion engine using a roughly triangular rotor in a shaped housing. Its rotor resembles a Reuleaux triangle but has different geometry and does not have constant width.
Ellipse: A closed curve whose points have a constant sum of distances from two foci. Most ellipses lack constant width, showing that convexity alone does not ensure it.
Kinematics of machinery: The study of motion in machines without regard to the forces causing it. Reuleaux’s work placed geometric curves within a systematic study of machine motion.
Circular arc: A continuous portion of a circle’s circumference. Three arcs of equal radius form the Reuleaux triangle’s boundary.
Rolling polygon: A polygon or curved shape that rolls while its center follows a path. The Reuleaux triangle can roll inside a square while maintaining contact with all four sides.

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