This article is about figure-eight shaped curves in algebraic geometry. For other uses, see Lemniscate (disambiguation).
The lemniscate of Bernoulli and its two foci
In algebraic geometry, a lemniscate (/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt,-kɪt/)[1] is any of several figure-eight or ∞-shaped curves.[2][3] The word comes from the Latin lēmniscātus, meaning "decorated with ribbons",[4] from the Greek λημνίσκος (lēmnískos), meaning "ribbon",[3][5][6][7] or which alternatively may refer to the wool from which the ribbons were made.[2]
Curves that have been called a lemniscate include three quartic plane curves: the hippopede or lemniscate of Booth, the lemniscate of Bernoulli, and the lemniscate of Gerono. The study of lemniscates (and in particular the hippopede) dates to ancient Greek mathematics, but the term "lemniscate" for curves of this type comes from the work of Jacob Bernoulli in the late 17th century.
^ abCite error: The named reference lemniscatomy was invoked but never defined (see the help page).
^ abErickson, Martin J. (2011), "1.1 Lemniscate", Beautiful Mathematics, MAA Spectrum, Mathematical Association of America, pp. 1–3, ISBN 9780883855768.
^lemniscatus. Charlton T. Lewis and Charles Short. A Latin Dictionary on Perseus Project.
In algebraic geometry, a lemniscate (/lɛmˈnɪskɪt/ or /ˈlɛmnɪsˌkeɪt, -kɪt/) is any of several figure-eight or ∞-shaped curves. The word comes from the Latin...
representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or...
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the...
mathematics, the lemniscate constant ϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter...
lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve...
In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex...
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied...
curve Hippopede Kampyle of Eudoxus Kappa curve LemniscateLemniscate of Booth Lemniscate of Gerono Lemniscate of Bernoulli Limaçon Cardioid Limaçon trisectrix...
< 0 the curve resembles a sideways figure eight, or lemniscate, and is often known as a lemniscate of Booth, after 19th-century mathematician James Booth...
Devil's curve Hippopede Kampyle of Eudoxus Klein quartic LemniscateLemniscate of Bernoulli Lemniscate of Gerono Limaçon Lüroth quartic Spiric section Squircle...
variation known as brimstone has a symbol combining a two-barred cross atop a lemniscate (🜏). In traditional skin treatment, elemental sulfur was used (mainly...
(n = −1/3) Cayley's sextet (n = 1/3) Cardioid (n = 1/2) Circle (n = 1) Lemniscate of Bernoulli (n = 2) The curves were first studied by Colin Maclaurin...
the term "lemniscate-oval vacuity" when first describing it, and subsequently referred to it simply as the "oval vacuity". The term lemniscate continued...
the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob Bernoulli in 1694. In 1695,...
quintic equations, and the property of the lemniscate of Bernoulli that a ball rolling down an arc of the lemniscate, under the influence of gravity, will...
himself suggested a design for a Periodic table in the style of a space lemniscate in 1898. Crookes was knighted in 1897. Crookes was named president of...
(complexity), a class of computational complexity sl (elliptic function), sine lemniscate function Special linear group in mathematics, denoted SLn Special linear...
intervals and among tuning systems. Lissajous orbit Blackburn pendulum Lemniscate of Gerono Spirograph Wikimedia Commons has media related to Lissajous...
can also be applied to the division of the lemniscate curve, which inspired Abel's theorem on lemniscate division. Another example is his publication...
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