I wonder if there are any interesting geometric (as opposed to number-theoretic) properties of what might be called Fermat's Last Theorem surfaces, i.e., $x^d + y^d = z^d$. Below are the surfaces for $d=2,4,6$.
They seem rather tame...
2026-04-05 21:46:22.1775425582
They seem rather tame...
Any interesting properties of Fermat's Last Theorem Surfaces?
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They seem rather tame...
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Each one of their horizontal cross-sections (with z being the vertical dimension, as in the $3$ figures you presented) is a superellipse (the case $d=4$ is called squircle), and are connected to the famous Gamma and Beta functions in terms of area. For rational values of the form $d=\dfrac1n$ , with $n\in\mathbb{N}$, they are linked to factorials and binomial coefficients.