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The exponential map of the Earth as viewed from the north pole is the polar azimuthal equidistant projection in cartography. In Riemannian geometry, an exponential map is a map from a subset of a tangent space T pM of a Riemannian manifold (or pseudo-Riemannian manifold) M to M itself. The (pseudo) Riemannian metric determines a canonical ...
In differential geometry, the exponential map is a generalization of the ordinary exponential function of mathematical analysis. Important special cases include: is a geodesic with initial velocity X, is sometimes also called the exponential map. The above two are special cases of this with respect to appropriate affine connections.
In mechanics and geometry, the 3D rotation group, often denoted SO (3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition. [1] By definition, a rotation about the origin is a transformation that preserves the origin, Euclidean distance (so it is an isometry), and orientation ...
Nicolas Chuquet used a form of exponential notation in the 15th century, for example 12 2 to represent 12x 2. [11] This was later used by Henricus Grammateus and Michael Stifel in the 16th century. In the late 16th century, Jost Bürgi would use Roman numerals for exponents in a way similar to that of Chuquet, for example iii 4 for 4 x 3 .
Exponential sheaf sequence. In mathematics, the exponential sheaf sequence is a fundamental short exact sequence of sheaves used in complex geometry. Let M be a complex manifold, and write OM for the sheaf of holomorphic functions on M. Let OM * be the subsheaf consisting of the non-vanishing holomorphic functions.
Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.