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The inverse function of the Gudermannian y=gd^(-1)phi gives the vertical position y in the Mercator projection in terms of the latitude phi and may be defined for 0<=x<pi/2 ...

An authalic latitude which is directly proportional to the spacing of parallels of latitude from the equator on an ellipsoidal Mercator projection. It is defined by ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

Consider a knot as being formed from two tangles. The following three operations are called mutations. 1. Cut the knot open along four points on each of the four strings ...

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 ...