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There are two theorems commonly known as Feuerbach's theorem. The first states that circle which passes through the feet of the perpendiculars dropped from the polygon ...

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.

An analytic refinement of results from complex analysis such as those codified by Picard's little theorem, Picard's great theorem, and the Weierstrass-Casorati theorem.

Specifying two adjacent side lengths a and c of a triangle (with a<c) and one acute angle A opposite a does not, in general, uniquely determine a triangle. If sinA<a/c, there ...

Combinatorial matrix theory is a rich branch of mathematics that combines combinatorics, graph theory, and linear algebra. It includes the theory of matrices with prescribed ...

The empire problem, also known as the m-pire problem) asks for the maximum number of colors needed to color countries such that no two countries sharing a common border have ...

If two intersections of each pair of three conics S_1, S_2, and S_3 lie on a conic S_0, then the lines joining the other two intersections of each pair are concurrent (Evelyn ...

Homogeneous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles. Barycentric coordinates normalized so ...