Search Results for ""

The Cayley-Menger determinant is a determinant that gives the volume of a simplex in j dimensions. If S is a j-simplex in R^n with vertices v_1,...,v_(j+1) and B=(beta_(ik)) ...

A plot in the complex plane of the points B(t)=S(t)+iC(t), (1) where S(t) and C(t) are the Fresnel integrals (von Seggern 2007, p. 210; Gray 1997, p. 65). The Cornu spiral is ...

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...

An algorithm used to recursively construct a set of objects from the smallest possible constituent parts. Given a set of k integers (a_1, a_2, ..., a_k) with a_1<a_2<...<a_k, ...

There are at least three theorems known as Jensen's theorem. The first states that, for a fixed vector v=(v_1,...,v_m), the function |v|_p=(sum_(i=1)^m|v_i|^p)^(1/p) is a ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

The Riemann theta function is a complex function of g complex variables that occurs in the construction of quasi-periodic solutions of various equations in mathematical ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...