Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.
Why Hacker News points people here: HN points to it as a visual teaching resource for Fourier series, and as a reference when epicycles come up as analogies.
“It's similar to Mathologer's "Epicycles, complex Fourier series and Homer Simpson's orbit"”HN comment, 2022
“It's similar to Mathologer's "Epicycles, complex Fourier series and Homer Simpson's orbit"”
Similar visual exposition of Fourier series with epicycles.
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For an additional video exposition, I also like Eugene Khutoryansky's "Fourier Transform, Fourier Series, and frequency spectrum" link In particular, the visualization of the addition of sine waves of different frequencies in three dimensions is pretty spectacular. It's similar to Mathologer's "Epicycles, complex Fourier series and Homer Simpson's orbit": this video
Cites itlisperApr 2022
Epicycles can fit any data, as an analogy for supersymmetry.
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Falsifying supersymmetry is like falsifying Ptolemaic epicycles. You can never falsify it with data because epicycles can always be constructed to fit any data set [1]. Likewise, a sypersymmetric theory can be constructed to fit any set of parameters. But fitting the data is not enough. You have to fit the data with substantially fewer parameters than data points. That's the challenge. [1] this video
Cites itadolphJul 2023
“Teaching Fourier series”
Linked as a teaching resource for Fourier series.
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> replicate the elaborate machines that engrave currency I think you may refer to a rose engine, which in operation is very close to a dimensional spirograph. A modern variant might be a core-xy open etch-a-sketch using those LCD writing tablets and a set of physical gears and pins that would control the stylus' motion, maybe powered by a folding handcrank like the Panic Playdate. It might even be a tool for teaching the Fourier series. rose engine: link core-xy: link LCD writing tablet: link Panic Playdate: link Teaching Fourier series: this video Also, projects on Hackaday: link
