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A function f is topologically transitive if, given any two intervals U and V, there is some positive integer k such that f^k(U) intersection V!=emptyset. Vaguely, this means ...

A surface of revolution obtained by rotating a closed plane curve about an axis parallel to the plane which does not intersect the curve. The simplest toroid is the torus. ...

A ring torus constructed out of a square of side length c can be dissected into two squares of arbitrary side lengths a and b (as long as they are consistent with the size of ...

If one part of the total intersection group of a curve of order n with a curve of order n_1+n_2 constitutes the total intersection with a curve of order n_1, then the other ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

The space E of a fiber bundle given by the map f:E->B, where B is the base space of the fiber bundle.

A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected ...

A trace form on an arbitrary algebra A is a symmetric bilinear form (x,y) such that (xy,z)=(x,yz) for all x,y,z in A (Schafer 1996, p. 24).

The evolute of the tractrix given by parametric equations x = t-tanht (1) y = secht (2) is the catenary x_e = t (3) y_e = cosht. (4)

The tractrix spiral is a spiral with parametric equations x(t) = acostcos(t-tant) (1) y(t) = acostsin(t-tant) (2) for t in [0,pi/2). It is also known as the polar tractrix or ...