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One name for the figure used by Euclid to prove the Pythagorean theorem.

A metric space X is boundedly compact if all closed bounded subsets of X are compact. Every boundedly compact metric space is complete. (This is a generalization of the ...

A short theorem used in proving a larger theorem. Related concepts are the axiom, porism, postulate, principle, and theorem. The late mathematician P. Erdős has often been ...

Every odd integer n is a prime or the sum of three primes. This problem is closely related to Vinogradov's theorem.

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...

The rotation vector of the trihedron of a curve with curvature kappa!=0 when a point moves along a curve with unit speed. It is given by D=tauT+kappaB, (1) where tau is the ...

A pair (M,omega), where M is a manifold and omega is a symplectic form on M. The phase space R^(2n)=R^n×R^n is a symplectic manifold. Near every point on a symplectic ...

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).

A specific type of ultraproduct that can be used to construct nonstandard universes and obtain the transfer principle as a corollary of Łoś' theorem for ultraproducts.

The 10_3 configuration of ten lines intersecting three at a time in 10 points which arises in Desargues' theorem. Its Levi graph is the Desargues graph.