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Every finite-dimensional Lie algebra of characteristic p!=0 has a faithful finite-dimensional representation.

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

The circumcircle of the Johnson triangle DeltaJ_AJ_BJ_C has center at the orthocenter H of the reference triangle and radius R, where R is the circumradius of the reference ...

A transformation of an algebraic curve which is of the same type as its inverse. A Jonquière's transformation is always factorable.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

In Kepler's 1619 book Harmonice Mundi on tilings, he discussed a tiling built with pentagons, pentagrams, decagons, and "fused decagon pairs." He also called them "monsters." ...

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 ...

A list of problems in low-dimensional topology maintained by Kirby (1995). The list currently runs about 380 pages.

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...