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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 ...
The Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble ...
Limacon Evolute The catacaustic of a circle for a radiant point is the limaçon evolute. It has parametric equations x = (a[4a^2+4b^2+9abcost-abcos(3t)])/(4(2a^2+b^2+3abcost)) ...
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