Les Jones

Word of the Day > Word of the Day: Reuleaux Triangle

A mathematical definition here, and here's a more readable one:

A Reuleaux polygon is a polygon that is a curve of constant width - that is, a curve in which all diameters are the same length. The best-known version is the Reuleaux triangle. Both are named after Franz Reuleaux, a 19th-century German engineer who did pioneering work on ways that machines translate one type of motion into another, although it was known before his time.

The Reuleaux triangle is the simplest nontrivial example of a curve of constant width - a curve in which the distance between two opposite parallel tangent lines to its boundary is the same, regardless of the direction of those two parallel lines. (The trivial example would be a circle.)

This is how you can draw the triangle:

One reason it's interesting is that a drill bit constructed in the shape of an offset Reuleaux triangle can bore a square hole:

Other interesting properties (from Wikipedia):

• Because all of its diameters are the same length, the Reuleaux triangle - actually, all Reuleaux polygons - is the answer to the Mensa-like question "Other than as a circle, what shape can you make a manhole cover so that it cannot fall down through the hole?"
• The rotor of the Wankel engine is a Reuleaux triangle.

Hat tip to Grant Cunningham.

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