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All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...

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 ...

The dual of Pascal's theorem (Casey 1888, p. 146). It states that, given a hexagon circumscribed on a conic section, the lines joining opposite polygon vertices (polygon ...

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

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

Alexandrov's theorem addresses conditions under which a polygon will fold into a convex polyhedron (Malkevitch).

Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the ...

A theorem which treats constructions of fields of field characteristic p.

The most general form of Lagrange's group theorem, also known as Lagrange's lemma, states that for a group G, a subgroup H of G, and a subgroup K of H, (G:K)=(G:H)(H:K), ...