FRIDAY SURPRISE: How do you drill a square hole?

No, I'm not talking about a mortising chisel, or a broach - I mean a real drill for square holes. They do exist!

A bit that drills square holes ... it defies common sense. How can a revolving edge cut anything but a circular hole? Not only do such bits exist (as well as bits for pentagonal, hexagonal and octagonal holes), but they derive their shape from a simple geometric construction known as a Reuleaux triangle (after Franz Reuleaux, 1829-1905).


To construct a Reuleaux triangle, start with an equilateral triangle of side s (Figure 1). With a radius equal to s and the center at one of the vertices, draw an arc connecting the other two vertices. Similarly, draw arcs connecting the endpoints of the other two sides. The three arcs form the Reuleaux triangle. One of its properties is that of constant width, meaning the figure could be rotated completely around between two parallel lines separated by distance s.


Click here for a scholarly (i.e., mathematic) explanation; click here to see a more down-to-earth explanation (including an animation that will make all clear.)

-=[ Grant ]=-

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