“Why are manhole covers round?” The Reuleaux Triangle (1-26 thru 2-1)

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“Why are manhole covers round?” This is a standard interview question to get a sense for an interview candidate's ability to think on his or her feet outside of their area of expertise. The way the candidate approaches the problem, thinks of and presents potential solutions, defends them, or discards them are all relevant to the interviewer.

The Mathletes explored this problem first hand with the simulated sewer and manholes I created in the shape of circles, squares, and a Reuleaux triangle. I put a Lego person in the sewer to model the effects that a 100 pound manhole would have on a sewer worker if it fell. They found out that a round manhole cover can't fall into the hole it covers. Also, heavy, round manhole covers are easier for one person to move by standing it on end and rolling. Also, you don't have to "align" a manhole cover to it's hole. Any orientation will do. I also believe that round manhole covers are easier to manufacture.

Now for the fun part: I told them that when I design my Mathlete City, its manhole covers would be in the shape of a Reuleaux triangle.

I taught them how to construct the Reuleaux. Construct an equilateral triangle. On each vertex, center a compass, and draw an arc the short distance between the other two vertices. The perimeter will be three nonconcentric arcs. It is not a circle, but, like a circle, it has constant width, no matter how it is oriented.

The most famous use for a Reuleaux triangle is the Wankel engine. The Wankel engine is a type of internal combustion engine which uses a rotary design to convert pressure into a rotating motion instead of using reciprocating pistons. See the pdf file attached.         This design delivers smooth high-rpm power from a compact size. Since its introduction the engine has been commonly referred to as the rotary engine, though this name is also applied to several completely different designs.

The engine was invented by German engineer Felix Wankel. Because of their compact design, Wankel rotary engines have been installed in a variety of vehicles and devices such as automobiles including racing cars, along with aircraft, go-karts, personal water craft, chain saws, and auxiliary power units. The most extensive automotive use of the Wankel engine has been by the Japanese company Mazda.

Reuleaux triangles are also used as a bit that drills square holes. See this terrific video.

http://www.wonderhowto.com/how-to/video/how-to-drill-a-square-hole-167997/view/

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