Lemniscate of Leaf Function

A lemniscate is a curve defined by two foci, F1 and F2. If the distance between the focal points of F1 − F2 is 2a (a: constant), then any point P on the lemniscate curve satisfy the equation PF1 · PF2 = a2. Jacob Bernoulli first described the lemniscate in 1694. The Fagnano discovered the double angle formula of the lemniscate (1718). The Euler extended the Fagnano’s formula to a more general addition theorem (1751). The lemniscate function was...