Search Results for ""

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

There are several theorems that generally are known by the generic name "Pappus's Theorem." They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

The reciprocity theorem for x^8=q (mod p).

Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin(2x) = 2sinxcosx (1) cos(2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

An angle theta drawn on the coordinate plane is said to be in standard position if its initial side lies on the positive x-axis so that its vertex coincides with the origin ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...