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The squeeze theorem, also known as the squeezing theorem, pinching theorem, or sandwich theorem, may be stated as follows. Let there be two functions f_-(x) and f_+(x) such ...

The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...

The Heine-Borel theorem states that a subspace of R^n (with the usual topology) is compact iff it is closed and bounded. The Heine-Borel theorem can be proved using the ...

Jackson's theorem is a statement about the error E_n(f) of the best uniform approximation to a real function f(x) on [-1,1] by real polynomials of degree at most n. Let f(x) ...

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

If J is a simple closed curve in R^2, then the Jordan curve theorem, also called the Jordan-Brouwer theorem (Spanier 1966) states that R^2-J has two components (an "inside" ...

A theorem that guarantees that the trajectory of Langton's ant is unbounded.

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

A generalization of Turán's theorem to non-complete graphs.