Reuleaux Triangle - Other Uses

Other Uses

• The rotor of the Wankel engine is easily mistaken for a Reuleaux triangle but its curved sides are somewhat flatter than those of a Reuleaux triangle and so it does not have constant width.
• The Watts Brothers Tool Works square drill bit has the shape of a Reuleaux triangle and can, if mounted in a special chuck which allows for the bit not having a fixed centre of rotation, drill a hole that is nearly square; the corners of the square are slightly rounded, as can be seen by tracing any vertex in this figure, and the drill bit covers 0.9877... of the area of the square. The Harry Watt square is often used in mortising Other Reuleaux polygons are used to drill pentagonal, hexagonal, and octagonal holes.
• A Reuleaux triangle (along with all other curves of constant width) can roll but makes a poor wheel because it does not roll about a fixed center of rotation. An object on top of rollers with cross-sections that were Reuleaux triangles would roll smoothly and flatly, but an axle attached to Reuleaux triangle wheels would bounce up and down three times per revolution. This concept was used in a science fiction short story by Poul Anderson titled "The Three-Cornered Wheel."
• Several pencils are manufactured in this shape, rather than the more traditional round or hexagonal barrels. They are usually promoted as being more comfortable or encouraging proper grip, as well as being less likely to roll off tables (since the center of gravity moves up and down more than a rolling hexagon).
• The shape is used for signage for the National Trails System administered by the United States National Park Service, as well as the logo of Colorado School of Mines and the Connecticut Collegiate Mathematics Competition.
• Valve covers used in the Mission Bay Project of San Francisco to differentiate reclaimed water from potable water are in the shape of a Reuleaux triangle.

• Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter is an equidiagonal kite that can be inscribed into a Reuleaux triangle.