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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 hippopede was studied by Proclus (5th century), but the term "lemniscate" was not used until the work of Jacob Bernoulli in the late 17th century.
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F 1 and F 2, known as foci, at distance 2c from each other as the locus of points P so that PF 1 ·PF 2 = c 2. The curve has a shape similar to the numeral 8 and to the ∞ symbol.
The lemniscate of Gerono. In algebraic geometry, the 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 shaped like an symbol, or figure eight. It has equation
Kappa curve; Lemniscate. Lemniscate of Booth; Lemniscate of Gerono; ... An elementary treatise on cubic and quartic curves by Alfred Barnard Basset (1901) online at ...
When d > 0 the curve has an oval form and is often known as an oval of Booth, and when d < 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 who studied them.
This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves. ... Lemniscate of Gerono. Lemniscate of Bernoulli. Limaçon. Cardioid.
The lemniscate sine (red) and lemniscate cosine (purple) applied to a real argument, in comparison with the trigonometric sine y = sin(πx/ϖ) (pale dashed red).. In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli.
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity.This symbol is also called a lemniscate, [1] after the lemniscate curves of a similar shape studied in algebraic geometry, [2] or "lazy eight", in the terminology of livestock branding.