A lemniscate is a mathematical curve shaped like a figure eight.
Lemniscate may also refer to:
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation.
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 locus of points P so that PF1·PF2 = c2. The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is from lemniscatus, which is Latin for "decorated with hanging ribbons". It is a special case of the Cassini oval and is a rational algebraic curve of degree 4.
In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials with rational coefficients.
The infinity symbol is a mathematical symbol 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 "lazy eight", in the terminology of livestock branding.
Binomial may refer to:
In mathematics, the lemniscate constantϖ is a transcendental mathematical constant that is the ratio of the perimeter of Bernoulli's lemniscate to its diameter, analogous to the definition of π for the circle. Equivalently, the perimeter of the lemniscate is 2ϖ. The lemniscate constant is closely related to the lemniscate elliptic functions and approximately equal to 2.62205755. The symbol ϖ is a cursive variant of π; see Pi § Variant pi.
In mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others.
In algebraic geometry, a lemniscate is any of several figure-eight or ∞-shaped curves. The word comes from the Latin "lēmniscātus" meaning "decorated with ribbons", from the Greek λημνίσκος meaning "ribbon", or which alternatively may refer to the wool from which the ribbons were made.
In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n.
Bernoulli can refer to:
In complex analysis (a branch of mathematical analysis), the pseudo-zero set or root neighborhood of a degree-m polynomial p(z) is the set of all complex numbers that are roots of polynomials whose coefficients differ from those of p by a small amount. Namely, given a norm |·| on the space of polynomial coefficients, the pseudo-zero set is the set of all zeros of all degree-m polynomials q such that |p − q| (as vectors of coefficients) is less than a given ε.
This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves.
In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates
In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest-order terms of F form a polynomial divisible by x2 + y2. More precisely, if F = Fn + Fn−1 + ... + F1 + F0, where each Fi is homogeneous of degree i, then the curve F(x, y) = 0 is circular if and only if Fn is divisible by x2 + y2.
Alexandre Eremenko is a Ukrainian-American mathematician who works in the fields of complex analysis and dynamical systems. He is a grandnephew of a Marshal of the Soviet Union Andrey Yeryomenko.
SLH may refer to: