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Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

The German mathematician Kronecker proved that all the Galois extensions of the rationals Q with Abelian Galois groups are subfields of cyclotomic fields Q(mu_n), where mu_n ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

The distance between two skew lines with equations x = x_1+(x_2-x_1)s (1) x = x_3+(x_4-x_3)t (2) is given by D=(|(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]|)/(|(x_2-x_1)x(x_4-x_3)|) (3) ...

Line segment picking is the process of picking line segments at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a ...