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The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

The three points determined on three coplanar edges of a tetrahedron by the external bisecting planes of the opposite dihedral angles are collinear. Furthermore, this line ...

A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

A topological space that is not connected, i.e., which can be decomposed as the disjoint union of two nonempty open subsets. Equivalently, it can be characterized as a space ...

Two sextuples of skew lines on the general cubic surface such that each line of one is skew to one line in the other set. In all, there are 30 points, with two lines through ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

Let G be a group and S be a topological G-set. Then a closed subset F of S is called a fundamental domain of G in S if S is the union of conjugates of F, i.e., S= union _(g ...

A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as A_y=ay^3+by^2+cy+d. The volume of such a solid is the same ...

Let M be a bounded set in the plane, i.e., M is contained entirely within a rectangle. The outer Jordan measure of M is the greatest lower bound of the areas of the coverings ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...