Lemniscate

In mathematics, a lemniscate is a type of curve described by a Cartesian equation of the form:

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:(x^2 + y^2)^2 = a^2 (x^2 - y^2)

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Graphing this equation produces a curve similar to infty. The curve has become a symbol of infinity and is widely used in math. The symbol itself is sometimes referred to as the lemniscate. Its Unicode representation is ∞ (∞).

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The lemniscate was first described in 1694 by Jakob Bernoulli 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. A lemniscate, by contrast, is the locus of points for which the product of these distances is constant. Bernoulli called it the lemniscus, which is Latin for 'pendant ribbon'.

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The lemniscate can be obtained as the inverse transform of a hyperbola, with the inversion circle centered at the center of the hyperbola (bisector of its two foci).

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Curve: In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. Simple examples are the circle or the straight line. A large number of other curves have been studied in geometry....

Cartesian: Cartesian means of or relating to the French philosopher and mathematician René Descartes—from his name—Rene Des-Cartes. It may refer to:...

Equation: :This article is about equations in mathematics. For equations in chemistry, see chemical equation....