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. A… More >
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