Lamé's special quartic with "radius" 1. Lamé's special quartic , named after Gabriel Lamé , is the graph of the equation
x
4
+
y
4
=
r
4
{\displaystyle x^{4}+y^{4}=r^{4}}
where
r
>
0
{\displaystyle r>0}
[ 1] square with "sides" of length
2
r
{\displaystyle 2r}
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
^ Oakley, Cletus Odia (1958), Analytic Geometry Problems , College Outline Series, vol. 108, Barnes & Noble, p. 171 ^ Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English ISBN 9780883855119
