TITLE: The graph of $x^{n}+y^{n}=r^{n}$ for sufficiently large $n$
QUESTION [16 upvotes]: The graph of the function $x^{n}+y^{n}=r^{n}$ for certain large values of $n$ looks suspiciously like a square.
See this page from wolframalpha. Have any results been proven regarding this observation? What do we call this figure anyway?

REPLY [8 votes]: Sometimes it's called a superellipse - see, e.g., http://en.wikipedia.org/wiki/Superellipse