Lemniscate

In algebraic geometry, a lemniscate (from Latin lēmniscātus meaning "decorated with ribbons") may refer to any of several figure-eight or ∞ shaped curves:

• The lemniscate of Bernoulli, often simply called the lemniscate, the locus of points whose product of distances from two foci equals the square of half the interfocal distance
• The lemniscate of Gerono, the zero set of the quartic polynomial x⁴ − x² + y²
• The lemniscate of Booth, the zero set of the quartic polynomial (x² + y²)² − cx² − dy² with d < 0. When d = −c this coincides with the lemniscate of Bernoulli
• Watt's curve, a curve formed a mechanical linkage.

It may also refer to:

• Polynomial lemniscate, the set of complex numbers for which a given polynomial has a constant absolute value
• The infinity symbol ∞, sometimes called a lemniscate because of its shape

See also

• Analemma, the figure-eight shaped curve traced by the noontime positions of the sun in the sky over the course of a year
• Lorenz attractor, a three-dimensional dynamic system exhibiting a lemniscate shape
• The lemniscate constants, numbers that arise in evaluating the arc length of a lemniscate of Bernoulli