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An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

The orthogonal decomposition of a vector y in R^n is the sum of a vector in a subspace W of R^n and a vector in the orthogonal complement W^_|_ to W. The orthogonal ...

A skew polygon such that every two consecutive sides (but no three) belong to a face of a regular polyhedron. Every regular polyhedron can be orthogonally projected onto a ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

Given a plane ax+by+cz+d=0 (1) and a point x_0=(x_0,y_0,z_0), the normal vector to the plane is given by v=[a; b; c], (2) and a vector from the plane to the point is given by ...

A map defined by one or more polynomials. Given a field K, a polynomial map is a map f:K^n->K^m such that for all points (x_1,...,x_n) in K^n, ...

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any ...

The regular skew icosahedron is a six-dimensional regular polytope that is just as symmetric as the Platonic icosahedron, but having different angles (Coxeter 1950; Coxeter ...