Are there equations for general shapes (not necessarily regular)?

Asked May 01 '23 at 11:50

Active May 01 '23 at 13:54

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I was playing around on DESMOS and I discovered an equation for a triangle. So I got curious and was wondering if there are equations for other shapes (not necessarily regular) ? For example, a circle has the equation $x^2+y^2=a$, a square has the equation $\lim_{n \to \infty} x^n+y^n=a$ or an irregular triangle (which I discovered) has the equation $\lim_{n\to \infty}x^n+y^n=x+y$? And by extension is there any way to create the same shapes but then regular?

edited May 01 '23 at 12:50

Jean Marie

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asked May 01 '23 at 11:50

d0uble_a_b4ttery

I have suppressed tag "graph-theory" which deals with completely different "mathematical beings"... – Jean Marie May 01 '23 at 12:25
Do you mean equations for having polygons with rounded corners ? – Jean Marie May 01 '23 at 12:26
You can make regular stars. Maybe transforming part of the equation in the link will give you irregular shapes – Тyma Gaidash May 01 '23 at 12:27
Somewhat, although I'm not sure how to describe it cause for example, the equation of square 'approaches a perfect square' as $n$ goes to infinity – d0uble_a_b4ttery May 01 '23 at 12:29
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I have to wonder if this is relevant, given the proximity in time. – Xander Henderson May 01 '23 at 12:54
Ultimately this may lead to Fourier series drawing (YouTube video), though I'm not sure if that's beyond what you intended. – nickgard May 01 '23 at 13:10
The “If you are willing to use limits” answer is not visible to me/others, but did appear in the inbox as I followed this question. Why? – Тyma Gaidash May 01 '23 at 16:22

Are there equations for general shapes (not necessarily regular)?

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