First Shape Found That Can’t Pass Through Itself | Quanta Magazine

First Shape Found That Can’t Pass Through Itself

A geometry problem that originated with a royal bet has been solved after more than three centuries.

Imagine holding two equal-size dice, is it possible to bore a tunnel through one die that’s big enough for the other to slide through? Many would say "no".

In the late 1600s, Prince Rupert of the Rhine was involved in a bet regarding this problem. The mathematician John Wallis proved mathematically that a straight tunnel in the direction of one of the cube’s inner diagonals can be made wide enough to allow another cube through.

A tunnel can be made wide enough to allow another cube through if drilled in the direction of one of the cube’s inner diagonals.

Author's summary: Geometry problem solved.

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Quanta Magazine Quanta Magazine — 2025-10-24