Lamé's special quartic
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Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation
- <math>x^4 + y^4 = r^4</math>
where <math>r > 0</math>.<ref>Template:Citation.</ref> It looks like a rounded square with "sides" of length <math>2r</math> and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a superellipse.<ref>Template:Citation.</ref>
Because of Pierre de Fermat's only surviving proof, that of the n = 4 case of Fermat's Last Theorem, if r is rational there is no non-trivial rational point (x, y) on this curve (that is, no point for which both x and y are non-zero rational numbers).