Lemniscate of Leaf Function

A lemniscate is a curve defined by two foci, F1 and F2. If the distance between focal points of - F2 2a (a: constant), then any point P on satisfy equation PF1 PF2 = a^2. Jacob Bernoulli first described in 1694. The Fagnano discovered double angle formula lemniscate(1718). Euler extended Fagnano's to more general addition theorem(1751). function was subsequently proposed Gauss around year 1800. These insights are summarized Jacobi as theory elliptic functions. leaf an function. Some formulas functions have been presented previous papers; these included theorem this its application nonlinear equations. In paper, geometrical properties at n 2 geometric relation theta arc length l using curve. relationship sleaf2(l) cleaf2(l) derived lemniscate, similarity triangles, Pythagorean theorem. literature, for (or functions, sl(l) cl(l)) has analytically; however, it not geometrically.