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Fast Fourier Analysis in action. Any complex waveform, sound, or shape can be perfectly reconstructed as the sum of simple rotating circles (epicycles).

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Massimo

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A square is constructed using its Fourier series (represented by sums of circles rotating around circles), then the higher order (smaller, faster rotation) circles are removed in turn. Credit: generomics
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A square is constructed using its Fourier series (represented by sums of circles rotating around circles), then the higher order (smaller, faster rotation) circles are removed in turn. Credit: generomics

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Thanks to a complex mathematical algorithm, these plastic shapes follow a very specific route as they roll. In fact, researchers have shown that a shape can be designed to follow almost any path you can think of.
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Mathematics. Epicycles. Fourier series. Polar bear synthesis. By Daniel Mentrard, Daniel Mentrard, Used with permission.
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Thanks to a complex mathematical algorithm, these plastic shapes follow a very specific route as they roll. In fact, researchers have shown that a shape can be designed to follow almost any path you can think of. Read the associated nature paper: 🔒
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A rotating ball casts a shadow that perfectly matches a mass on a spring, revealing how circular motion and simple harmonic motion are linked. A visual proof of sine-wave physics in action.
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A rotating ball casts a shadow that perfectly matches a mass on a spring, revealing how circular motion and simple harmonic motion are linked. A visual proof of sine-wave physics in action.

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A rotating ball casts a shadow that perfectly matches a mass on a spring, revealing how circular motion and simple harmonic motion are linked. A visual proof of sine-wave physics in action.
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Made a simple toy to morph any text with Fourier transforms. Just enter any from/to text in any language and see it morphs: Bonus: Can share link with friends to send the exact message morph to them
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"transient processor" can be used to increase the intensity of S1 and S2 without affecting the rest of the waveform
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if the muses in any hercules live action adaption don’t sound like this then they can keep it. 🙂‍↕️
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if the muses in any hercules live action adaption don’t sound like this then they can keep it. 🙂‍↕️

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