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Prince Rupert's problem




The problem of pushing a cube through a hole in another cube of equal or less size; it is named after Prince Rupert (1619–1682), a nephew of England's King Charles I, who won a wager that a hole could be made in one of two equal cubes large enough for the other cube to slide through.

The mathematics of cubes passing through cubes was considered by John Wallis. Later, in 1816, a solution was published posthumously by the Dutch mathematician Pieter Nieuwland (1764–1794) to the question of what is the largest cube that can be pass through a cube of unit side. Nieuwland answered this by finding the largest square that fits inside a unit cube. When viewed from directly above one apex, a unit cube has the outline of a regular hexagon of side √3/√2. The largest square that will go into a cube has a face that can be inscribed within this hexagon; the length of its edge is 3√2/4 = 1.0606601...


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