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A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

An Eulerian cycle, also called an Eulerian circuit, Euler circuit, Eulerian tour, or Euler tour, is a trail which starts and ends at the same graph vertex. In other words, it ...

A plane curve proposed by Descartes to challenge Fermat's extremum-finding techniques. In parametric form, x = (3at)/(1+t^3) (1) y = (3at^2)/(1+t^3). (2) The curve has a ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

An optical illusion named after British psychologist James Fraser, who first studied the illusion in 1908 (Fraser 1908). The illusion is also known as the false spiral, or by ...

Gelfond's theorem, also called the Gelfond-Schneider theorem, states that a^b is transcendental if 1. a is algebraic !=0,1 and 2. b is algebraic and irrational. This provides ...

The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

There are no fewer than two closely related but somewhat different notions of gerbe in mathematics. For a fixed topological space X, a gerbe on X can refer to a stack of ...