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The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

A plane parallel to two (or more) skew lines, also called a director plane. The orientation of a director is fixed, but it is specified uniquely only if a point lying on it ...

A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure ...

Given a point set P={x_n}_(n=0)^(N-1) in the s-dimensional unit cube [0,1)^s, the star discrepancy is defined as D_N^*(P)=sup_(J in Upsilon^*)D(J,P), (1) where the local ...

A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

The imaginary number i=sqrt(-1), i.e., the square root of -1. The imaginary unit is denoted and commonly referred to as "i." Although there are two possible square roots of ...