A regular Reuleaux polygon has sides of equal length. More generally, when a Reuleaux polygon has sides that can be split into arcs of equal length, the convex hull of the arc endpoints is a Reinhardt …

The Reuleuaux triangle —, the simplest figure of constant width will help us to drill square holes. If one moves the center of the this «triangle» along some trajec­tory, its vertices will draw almost a square …

If we now move the centroid of the Reuleaux Triangle along a certain closed curve and rotate the triangle continually, the Reuleraux Triangle will sweep out a square with slightly rounded corners.

The geometric centroid does not stay fixed as the triangle is rotated, nor does it move along a circle. In fact, the path consists of a curve composed of four arcs of an ellipse (Wagon 1991). For a bounding …

As the reuleaux turns in the square, watch the motion of the centroid. For every rotation of the reuleaux, the centroid makes three revolutions in the opposite direction, and its path is not circular.

Here is a page showing a rolling Reuleaux Triangle and here is one showing it rotating (and thus how a drill bit can be made to drill a nearly square hole). It's easy to compute the area of a Reuleaux triangle.

In engineering, Felix Heinrch Wankel (1902-1988) designed a rotor engine which has the shape of a Reuleaux triangle inscribed in a chamber, rather than the usual piston, cylinder, and mechanical …

Geometry forum discussion on the Reuleux triangle and its ability to drill out (most of) a square hole. A magic geometric constant optimized by the Reuleaux triangle.

Jul 25, 2022 · As noted earlier, the Reuleaux Triangle is one of the best ways to create a square with small curved edges. The constant curve width and irregular rotating motion help in carving out a …

Several types of machinery take the shape of the Reuleaux triangle, based on its property of being able to rotate within a square. The Watts Brothers Tool Works square drill bit has the shape of a Reuleaux …