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A nonplanar graph is a graph that is not planar. The numbers of simple nonplanar graphs on n=1, 2, ... nodes are 0, 0, 0, 0, 1, 14, 222, 5380, 194815, ... (OEIS A145269), ...

A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

The necessary condition for the polychoron to be regular (with Schläfli symbol {p,q,r}) and finite is cos(pi/q)<sin(pi/p)sin(pi/r). Sufficiency can be established by ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=-alpha+/-ibeta (with alpha,beta>0).

A fixed point for which the stability matrix has both eigenvalues positive, so lambda_1>lambda_2>0.

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=alpha+/-ibeta (with alpha,beta>0).