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The triangular number T_n is a figurate number that can be represented in the form of a triangular grid of points where the first row contains a single element and each ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

Geometry

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspective axis or homology ...