1) Here is a mental exercise. First, imagine an equilateral triangle on a flat surface. Label the triangle’s corners A, B and C. Place one point of a compass on A and the other on B, and draw an arc from B to C. Draw similar arcs from C to A, and A to B. The result is an equilateral triangle whose corners are joined by arcs. What formula gives you the area of this curve-sided triangle? You may use paper to calculate.

2) What shape is produced if you rotate this curved triangle on a flat surface?

The answers to November’s puzzles were supplied in the November issue.

Here are the answers to this month’s puzzles:

1) The curved triangle you’ve imagined is called a Reuleaux triangle. If the straight length of its equilateral parent is x, we find the Reuleaux area by taking pi minus root 3, multiplying the result by x squared, then dividing by 2.

2) The area covered by rotating a Reuleaux triangle (as craftsmen will know) is a square! Well, not precisely a square, because of very slightly rounded corners. The actual area produced is 0.9877… of the area of a square. Close enough.

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