2021
DOI: 10.32604/cmes.2021.012383
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Lemniscate of Leaf Function

Abstract: A lemniscate is a curve defined by two foci, F 1 and F 2 . If the distance between the focal points of F 1 − F 2 is 2a (a: constant), then any point P on the lemniscate curve satisfy the equation PF 1 • PF 2 = a 2 . 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. Thes… Show more

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