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The locus of the centers of all circumconics that also pass through the orthocenter of a triangle (which, when not degenerate, are rectangular hyperbolas) is a circle through ...

The volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane. Proving the theorem for n=2 (where it is known as the ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

A geometric theorem related to the pentagram and also called the Pratt-kasapi theorem. It states ...

A theorem, also called a unicity theorem, stating the uniqueness of a mathematical object, which usually means that there is only one object fulfilling given properties, or ...

A theorem which asserts that if a sequence or function behaves regularly, then some average of it behaves regularly. For example, A(x)∼x implies A_1(x)=int_0^xA(t)dt∼1/2x^2 ...

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...

A theorem stating the existence of an object, such as the solution to a problem or equation. Strictly speaking, it need not tell how many such objects there are, nor give ...