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History

The lemniscate was first described in 1694 by Jakob Bernoulli, a Swiss mathematician born in 1654, as a modification of an ellipse, which is the locus of points for which the sum of the distances to each of two fixed focal points is a constant. The general properties of the lemniscate were discovered by Giovanni Fagnano in 1750. Euler's investigations of the arc length of the curve (1751) led to later work on elliptic functions. The Lemniscate of Bernoulli is a special case of a Cassinian Oval (Cassini 1680). The lemniscate is symmetric about the x-axis, the y-axis, and the origin.