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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 ...

If X is a locally compact T2-space, then the set C_ degrees(X) of all continuous complex valued functions on X vanishing at infinity (i.e., for each epsilon>0, the set {x in ...

A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

Tutte's wheel theorem states that every polyhedral graph can be derived from a wheel graph via repeated graph contraction and edge splitting. For example, the figure above ...

A reciprocity theorem for the case n=3 solved by Gauss using "integers" of the form a+brho, when rho is a root of x^2+x+1=0 (i.e., rho equals -(-1)^(1/3) or (-1)^(2/3)) and ...

For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals AB×CD+BC×DA=AC×BD (1) (Kimberling 1998, p. 223). ...

A theorem about (or providing an equivalent definition of) compact sets, originally due to Georg Cantor. Given a decreasing sequence of bounded nonempty closed sets C_1 ...

Frucht's theorem states that every finite group is the automorphism group of a finite undirected graph. This was conjectured by König (1936) and proved by Frucht (1939). In ...

Define E(x;q,a)=psi(x;q,a)-x/(phi(q)), (1) where psi(x;q,a)=sum_(n<=x; n=a (mod q))Lambda(n) (2) (Davenport 1980, p. 121), Lambda(n) is the Mangoldt function, and phi(q) is ...

For elliptic curves over the rationals Q, the group of rational points is always finitely generated (i.e., there always exists a finite set of group generators). This theorem ...