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Let x:U->R^3 be a regular patch, where U is an open subset of R^2. Then (partiale)/(partialv)-(partialf)/(partialu) = eGamma_(12)^1+f(Gamma_(12)^2-Gamma_(11)^1)-gGamma_(11)^2 ...

The low-level language of topology, which is not really considered a separate "branch" of topology. Point-set topology, also called set-theoretic topology or general ...

If two points A and A^' are inverse (sometimes called conjugate) with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

The Steiner deltoid is the envelope of the Simson lines of a triangle. Its circumcircle is the Steiner circle, and its incircle is the nine-point circle. The triangle formed ...

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

If ABB^' and AC^'C are straight lines with BC and B^'C^' intersecting at D and AB+BD=AC^'+C^'D, then AB^'+B^'D=AC+CD. The origin and some history of this theorem are ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...

An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication ...