Kazunori Shinohara*
CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.1, pp. 275-292, 2021, DOI:10.32604/cmes.2021.012383
Abstract 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
subsequently proposed by Gauss around the year 1800. These insights were summarized by Jacobi as the theory of
elliptic functions.… More >
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