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词条 Lamé's special quartic
释义

  1. References

Lamé's special quartic, named after Gabriel Lamé, is the graph of the equation

where .[1] 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.[2]

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).

References

1. ^{{citation|title=Analytic Geometry Problems|volume=108|series=College Outline Series|first=Cletus Odia|last=Oakley|publisher=Barnes & Noble|year=1958|page=171}}.
2. ^{{citation|title=The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English|series=MAA Spectrum|first=Steven|last=Schwartzman|publisher=Mathematical Association of America|year=1994|isbn=9780883855119|page=212|url=https://books.google.com/books?id=SRw4PevE4zUC&pg=PA212}}.
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