Two decades ago, the mathematician Moon Duchin spent her summers teaching geometry at Mathcamp, a program for mathematically talented teens. Campers contemplated notions such as how to prove whether a given shape could be cut up into triangles. Another favorite was a famous “decomposability” paradox.
“You can take a solid ball, cut it into five pieces that don’t overlap, move those pieces around and reconstruct two solid balls that are the same size
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