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About: Lamé's special quartic     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Abstraction100002137yago:Communication100033020yago:Equation106669864yago:MathematicalStatement106732169yago:Message106598915yago:Statement106722453yago:WikicatEquations New Facet based on Instances of this Class

Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation where . It looks like a rounded square with "sides" of length and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a superellipse. 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).