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Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

The parameter r (sometimes also denoted mu) in the logistic equation x_(n+1)=rx_n(1-x_n).

Each centered convex body of sufficiently high dimension has an "almost spherical" k-dimensional central section.

The radius of the smallest circle centered at one of the points of an N-cluster, which contains all the points in the N-cluster.

A hex number, also called a centered hexagonal number, is given by H_n = 1+6T_n (1) = 3n^2+3n+1, (2) where T_n=n(n+1)/2 is the nth triangular number and the indexing with ...

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The locus of lines meeting three given skew lines. ("Regulus" is also the name of the brightest star in the constellation Leo.)

A transformation of period 2.

The property of being the only possible solution (perhaps modulo a constant, class of transformation, etc.).

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...