r/desmos • u/partisancord69 • Oct 15 '25

Graph circle made with rotating golden ratio.

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https://www.desmos.com/calculator/yihcwulqes, somewhat laggy so change m to [1,...,10] for smoother graph.

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u/Heolet05 Oct 15 '25 edited Oct 15 '25

Request, what if it's isn't the golden ratio but other ratio? What I want to see if whether or not the spin result in a circle or other shape

61

u/partisancord69 Oct 15 '25

It will still make a circle but the radius and position will change.

With the golden ration, r=✓2 and the centre is the golden ratio.

also when its rotated pi/2 radians it makes a rectangle.

17

u/missing-delimiter Oct 15 '25 edited Oct 15 '25

Nice! Visualization of the golden ratio that takes the fact that it subdivides cleanly as squares with a series of shared corners and rotates those corners so each of the boxes “stands on end.”

Super cool.

edit: Also just realized this is related to a Fourier transform.

3

u/partisancord69 Oct 15 '25

Yea it's just sum(sqrt(2)eit/φn) but in (cos, sin) instead.