Lamé's special quartic

Lamé's special quartic with "radius" 1.

Lamé's special quartic is the graph of the equation

x^4 + y^4 = r^4

where r > 0.[1] It looks like a rounded square with "sides" of length 2r and centered on the origin. This curve is a squircle centered on the origin, and it is a special case of a super ellipse.[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).

References

  1. ↑ Oakley, Cletus Odia (1958), Analytic Geometry Problems, College Outline Series 108, Barnes & Noble, p. 171.
  2. ↑ Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, MAA Spectrum, Mathematical Association of America, p. 212, ISBN 9780883855119.
This article is issued from Wikipedia - version of the Sunday, January 31, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.