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In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

In finding the average area A^__R of a triangle chosen from a closed, bounded, convex region R of the plane, then A^__(T(R))=A^__R, for T any nonsingular affine ...

An arrangement of n>=3 points such that n-1 of them are collinear.

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

The radical circle of the Stammler circles has center at the nine-point center N, which is Kimberling center X_5. The radius is given by R_S = sqrt(R^2+ON^2) (1) = ...

Lines that intersect in a point are called intersecting lines. Lines that do not intersect are called parallel lines in the plane, and either parallel or skew lines in ...

Lachlan's term for a set of four lines, no three of which are concurrent.

The intersection of two sets A and B is the set of elements common to A and B. This is written A intersection B, and is pronounced "A intersection B" or "A cap B." The ...

Two distinct theorems are referred to as "the de Bruijn-Erdős theorem." One of them (de Bruijn and Erdős 1951) concerns the chromatic number of infinite graphs; the other (de ...