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The equation $x^n + y^n = 1$ has a familiar parametrized version for $n=2$, which is a circle $(\cos(\theta), \sin(\theta))$. For even n, the greater the value, the closer it comes to a square (infinite norm). Do you know an algebraic manner to parametrize it except for $(\cos^{\frac{2}{n}}(\theta), \sin^{\frac{2}{n}}(\theta))$? This version I mention previously seems inadequate for some regions of $\sin(\cdot)$ and $\cos(\cdot)$ domain.

Thank you for the help.

Bruno Lobo
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Bruno Peixoto
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  • I think that $|x|^n + |y|^n = 1$ is the equation of the curves you are think of, a parametrization can be found here: https://en.wikipedia.org/wiki/Superellipse#Mathematical_properties – Martin R Apr 08 '22 at 01:49
  • Great! I thank you, sir! – Bruno Lobo Apr 08 '22 at 19:02

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