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A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...

A triangle with side lengths a, b, and c and triangle area Delta satisfies a^2+b^2+c^2>=4sqrt(3)Delta. Equality holds iff the triangle is equilateral.

Every nonempty set of positive integers contains a smallest member.

The Werner formulas are the trigonometric product formulas 2sinalphacosbeta = sin(alpha-beta)+sin(alpha+beta) (1) 2cosalphacosbeta = cos(alpha-beta)+cos(alpha+beta) (2) ...

A nonconformal, equal-area projection which is a special case of the Bonne projection where one of the poles is taken as the standard parallel. Because of its heart shape, ...

The satellite knot of an unknot twisted inside a torus.

An open three-manifold which is simply connected but is topologically distinct from Euclidean three-space.

Maps between CW-complexes that induce isomorphisms on all homotopy groups are actually homotopy equivalences.

A theorem that classifies planar regular closed curves up to regular homotopy by their contour winding numbers (Whitney 1937). In his thesis, S. Smale generalized this result ...

The width of a box is the horizontal distance from side to side (usually defined to be greater than the depth, the horizontal distance from front to back).