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One of the eight regions of space defined by the eight possible combinations of signs (+/-,+/-,+/-) for x, y, and z.

Two or more lines or line segments which are perpendicular are said to be orthogonal.

A hyperbola for which the asymptotes are perpendicular, also called an equilateral hyperbola or right hyperbola. This occurs when the semimajor and semiminor axes are equal. ...

Two curves are tangent externally at a point P if they lie on opposite sides of their common tangent at P

Two curves are tangent internally at a point P if they lie on the same side of their common tangent at P

For a finite group G, let p(G) be the subgroup generated by all the Sylow p-subgroups of G. If X is a projective curve in characteristic p>0, and if x_0, ..., x_t are points ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

Bipolar coordinates are a two-dimensional system of coordinates. There are two commonly defined types of bipolar coordinates, the first of which is defined by x = ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...

Let alpha(z),gamma(z):(a,b)->R^3 be curves such that |gamma|=1 and alpha·gamma=0, and suppose that alpha and gamma have holomorphic extensions alpha,gamma:(a,b)×(c,d)->C^3 ...