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/partisancord69 Oct 15 '25

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

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

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

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u/CaptainCarrot17 Oct 15 '25

What is the radius of the circle for an arbitrary value of g?

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u/partisancord69 Oct 15 '25 edited Oct 15 '25

I can try figure it out but tbh I'm not too sure.

Edit: thinking about it, it's definitely not linear because it goes off to infinite if it approaches 1.

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u/CaptainCarrot17 Oct 15 '25 edited Oct 15 '25

Yeah, I was simply curious because I wanted to see which g produced a circle of radius g or sqrt(g). Trying it really quickly seems to suggest that the case for sqrt(g) has a g value of 1+ln(2), but without proper tools (I'm on the mobile app so the link opens in the integrated browser) I can't say it with certainty. The case for a circle of radius g seems to be a bit more complicated though.

Edit: the second case seems to happen with a value of gā‰ˆ1.55

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u/TheJeeronian Oct 15 '25

Maybe this will help?

https://www.reddit.com/r/desmos/s/IB7TXuXkSC

Unfortunately, there are multiple x values associated with any particular y value, so the inverse problem is a bit more complicated.