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A notation used to describe curves. The fundamental principle of Clebsch-Aronhold notation states that if each of a number of forms be replaced by a power of a linear form in ...

A tool with two arms joined at their ends which can be used to draw circles. In geometric constructions, the classical Greek rules stipulate that the compass cannot be used ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

The term "continuum" has (at least) two distinct technical meanings in mathematics. The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; ...

A set of n variables which fix a geometric object. If the coordinates are distances measured along perpendicular axes, they are known as Cartesian coordinates. The study of ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

In general, there are two important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first ...

The point on the positive ray of the normal vector at a distance rho(s), where rho is the radius of curvature. It is given by z = x+rhoN (1) = x+rho^2(dT)/(ds), (2) where N ...

Taking the ratio x/y of two numbers x and y, also written x÷y. Here, x is called the dividend, y is called the divisor, and x/y is called a quotient. The symbol "/" is called ...

Two metrics g_1 and g_2 defined on a space X are called equivalent if they induce the same metric topology on X. This is the case iff, for every point x_0 of X, every ball ...