J. Thomas Walker - Mathematics

Here are some math puzzles that I have found interesting, some I have solved, some I haven't.

1. What is the area of A in terms of r? Two versions of a figure of a square with circle arcs connecting opposite corners. In the first, regions are labeled A, B and C. In the second, corners and points of intersection labeled. The corners of the square are E, F, G, H and the arc intersections are J, K, L, M.

Two versions of a figure of a square with circle arcs connecting opposite corners. In the first, regions are labeled A, B and C. In the second, corners and points of intersection labeled. The corners of the square are E, F, G, H and the arc intersections are J, K, L, M.

Given the square EFGH with sides of length r and the circle segments HKJF, HLMF, EKLG and EJMG each with a radius of r and center at one of the corners. Hint, think about the problem in terms of the area's of the regions created by the square and arcs (see left figure).

2. How can this be true? Figures of triangles composed of partitions in different arrangements.

The four parts of the top figure are moved around in the bottom figure. The partitions are exactly the same as those used above. From where does the hole come?