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Given two closed curves, the circuminscribed curve is simultaneously inscribed in the outer one and circumscribed on the inner one.

The dimension of a special series can never exceed half its order.

In the plane, a closed curve is a curve with no endpoints and which completely encloses an area.

The inverse curve of the cochleoid r=(sintheta)/theta (1) with inversion center at the origin and inversion radius k is the quadratrix of Hippias. x = ktcottheta (2) y = kt. ...

Let AB and CD be dyads. Their colon product is defined by AB:CD=C·AB·D=(A·C)(B·D).

Given a Schwarz triangle (p q r), replacing each polygon vertex with its antipodes gives the three colunar spherical triangles (p q^' r^'),(p^' q r^'),(p^' q^' r), (1) where ...

The components of the gradient of the one-form dA are denoted A_(,k), or sometimes partial_kA, and are given by A_(,k)=(partialA)/(partialx^k) (Misner et al. 1973, p. 62). ...

A tensor-like coefficient which gives the difference between partial derivatives of two coordinates with respect to the other coordinate, ...

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

Two angles alpha and beta are said to be complementary if alpha+beta=pi/2. In other words, alpha and beta are complementary angles if they produce a right angle when combined.