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A root-finding algorithm also known as the tangent hyperbolas method or Halley's rational formula. As in Halley's irrational formula, take the second-order Taylor series ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The study of manifolds having a complete Riemannian metric. Riemannian geometry is a general space based on the line element ds=F(x^1,...,x^n;dx^1,...,dx^n), with F(x,y)>0 ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

The ith Stiefel-Whitney class of a real vector bundle (or tangent bundle or a real manifold) is in the ith cohomology group of the base space involved. It is an obstruction ...

A strong Riemannian metric on a smooth manifold M is a (0,2) tensor field g which is both a strong pseudo-Riemannian metric and positive definite. In a very precise way, the ...

For a scalar function f over a surface parameterized by u and v, the surface integral is given by Phi = int_Sfda (1) = int_Sf(u,v)|T_uxT_v|dudv, (2) where T_u and T_v are ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

The functions (also called the circular functions) comprising trigonometry: the cosecant cscx, cosine cosx, cotangent cotx, secant secx, sine sinx, and tangent tanx. However, ...