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Rolling Polygons Turn One Octave per Arch #polygons #math #music · XDL

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Rolling Polygons Turn One Octave per Arch #polyg…

Rolling Polygons Turn One Octave per Arch #polygons #math #music

@Anish

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Roll a wheel a quarter the size of a circle around its inside and a pen on its rim draws an ASTROID. Roll a wheel THREE quarters the size and — three laps later — it draws exactly the same curve. That is Bernoulli's double generation: radius r and radius R − r trace one

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@Q.E.D Insights

A mathematical construction in which one strip completes exactly ten turns. The polar angle of the generating curve is controlled by the exponential φ(θ) = (π/2) e^{-θ/8π}. Successive windings therefore nest inside one another, forming a compact layered rose with an

I asked Claude Opus 5.5 to compose piano music. Animation drawn using JavaScript.

opus 5.5 passed a real threshold at making music with code! this is one shot from asking "make some bass music with javascript" 🔊

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