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Define T as the set of all points t with probabilities P(x) such that a>t=>P(a<=x<=a+da)<P_0 or a<t=>P(a<=x<=a+da)<P_0, where P_0 is a point probability (often, the ...

The space join of a topological space X and a point P, C(X)=X*P.

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

Cauchy's integral formula states that f(z_0)=1/(2pii)∮_gamma(f(z)dz)/(z-z_0), (1) where the integral is a contour integral along the contour gamma enclosing the point z_0. It ...

A surface on which the Gaussian curvature K is everywhere positive. When K is everywhere negative, a surface is called anticlastic. A point at which the Gaussian curvature is ...

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

The evolute of a circle is a degenerate point at the origin.

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

Newton's method, also called the Newton-Raphson method, is a root-finding algorithm that uses the first few terms of the Taylor series of a function f(x) in the vicinity of a ...