VisuApps
Grasp mathematical theorems visually
Apps
Zeno's paradox to touch: step through manually or run automatically — the "while he was here, she was there" snapshots happen faster and faster. "Resolve" lets both move at constant speed, Achilles overtakes at the meeting point. With zoom/pan, time account and space-time window.
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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.
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The sum 1+2+…+n as a staircase — a second staircase rotates in from above and completes the rectangle.
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The hotel with infinitely many rooms is full — and still admits 1, n or infinitely many new guests. Three scenarios as a 3D move.
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The indirect proof with tiles: 2q² = p² splits the p² square into two equal halves, odd squares always keep a middle tile, p = 2a quarters the square and q turns even, so the stamp “reduced” breaks and the same figure returns one step smaller. In Try mode, test your own fractions: even 99/70 misses by exactly one tile.
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