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A branch of mathematics that is a sort of generalization of calculus. Calculus of variations seeks to find the path, curve, surface, etc., for which a given function has a ...

Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

A vector field v for which the curl vanishes, del xv=0.

A divergenceless vector field, also called a solenoidal field, is a vector field for which del ·F=0. Therefore, there exists a G such that F=del xG. Furthermore, F can be ...

A geodesic mapping f:M->N between two Riemannian manifolds is a diffeomorphism sending geodesics of M into geodesics of N, whose inverse also sends geodesics to geodesics ...

A generalized conformal mapping.

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...