Lemniscate

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

Related Topics:
Mathematics - Curve - Cartesian - Equation

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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 ∞ (∞).

Related Topics:
Symbol - Infinity - Unicode

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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'.

Related Topics:
1694 - Jakob Bernoulli - Ellipse - Locus - Distance - Constant - Latin

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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).

Related Topics:
Inverse transform - Hyperbola - Circle

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