Lemniscate elliptic functions: Difference between revisions

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They are doubly periodic (or elliptic) functions in the complex plane, with periods 2π''G'' and 2π''iG'', where [[Gauss's constant]] ''G'' is given by

:<math>G=\frac{2}{\pi}\int_0^1\frac{dt}{\sqrt{1-t^4}}= 0.8346\ldots</math>

===Arclength of lemniscate===

The lemniscate

:<math>(x^2+y^2)^2=x^2-y^2</math>

consists of the points such that the product of their distances from two the two points (&radic;2, 0), (&minus;&radic;2, 0) is the constant 1/2.

==See also==