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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 ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as ...

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, ...

The term "real line" has a number of different meanings in mathematics. Most commonly, "real line" is used to mean real axis, i.e., a line with a fixed scale so that every ...

An auxiliary latitude which gives a sphere having correct distances along the meridians. It is denoted mu (or omega) and is given by mu=(piM)/(2M_p). (1) M_p is evaluated for ...

A Tychonoff plank is a topological space that is an example of a normal space which has a non-normal subset, thus showing that normality is not a hereditary property. Let ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...