Banach–Tarski: 1 orange becomes 2

About this app

The proof of the Banach–Tarski paradox in six walk-through chapters: two rotations generate the free group (type words, the ball rotates along), the Cayley tree splits into five pieces, the Hilbert-Hotel trick unfolds one branch into almost everything — and finally the dust pieces reassemble into two oranges. Including the axiom of choice and the resolution of why no gold gets duplicated.

Subject: Visual proofs

More from Visual proofs

• Achilles and the Tortoise (Zeno)
• Little Gauss
• Hilbert's Hotel
• Why √2 is not rational

A VisuApp by heyprof: interactive, free in your browser, no sign-up. What is a VisuApp? · All apps