Lemniscate constant

In mathematics, the lemniscate constant $ϖ$ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of $π$ for the circle. Equivalently, the perimeter of the lemniscate $(x^{2}+y^{2})^{2}=x^{2}-y^{2}$ is $2 ϖ$ . The lemniscate constant is closely related to the lemniscate elliptic functions and approximately equal to 2.62205755. It also appears in evaluation of the gamma and beta function at certain rational values. The symbol $ϖ$ is a cursive variant of $π$ known as variant pi represented in Unicode by the character U+03D6 ϖ GREEK PI SYMBOL.

Sometimes the quantities $2 ϖ$ or $ϖ/2$ are referred to as the lemniscate constant.