Problem of the Week 1225

Square Peg in Square Hole

What is the side-length of the largest cube that can fit through a square hole drilled through a unit cube?

Precisely: We seek a hole in the cube (turning it into a topological torus) so that the new cube can fit through this hole.

Source: A Mathematical Space Odyssey, a very nice new book by Claudi Alsina and Roger Nelsen, published by the MAA. This problem has a long and interesting history, going back to about 1693.

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