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There are least two Bang's theorems, one concerning tetrahedra (Bang 1897), and the other with widths of convex domains (Bang 1951). The theorem of Bang (1897) states that ...

Let a Cevian PC be drawn on a triangle DeltaABC, and denote the lengths m=PA^_ and n=PB^_, with c=m+n. Then Stewart's theorem, also called Apollonius' theorem, states that ...

The Diophantine equation x^2+y^2=p can be solved for p a prime iff p=1 (mod 4) or p=2. The representation is unique except for changes of sign or rearrangements of x and y. ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

There are several theorems known as the "sandwich theorem." In calculus, the squeeze theorem is also sometimes known as the sandwich theorem. In graph theory, the sandwich ...

For omega a differential (k-1)-form with compact support on an oriented k-dimensional manifold with boundary M, int_Mdomega=int_(partialM)omega, (1) where domega is the ...

Consider the inequality sigma(n)<e^gammanlnlnn for integer n>1, where sigma(n) is the divisor function and gamma is the Euler-Mascheroni constant. This holds for 7, 11, 13, ...