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The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

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 ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...

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 ...