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The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...

To each epsilon>0, there corresponds a delta such that ||f-g||<epsilon whenever ||f||=||g||=1 and ||(f+g)/2||>1-delta. This is a geometric property of the unit sphere of ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

A horizontal line placed under a symbol to indicate some special property. Underscores are sometimes used instead of over-arrows or bold typeface to indicate a vector, for ...

A vector basis of a vector space V is defined as a subset v_1,...,v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1,v_2,...,v_n) is a list ...

Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...

If a line intersects one of two parallel lines, both of which are coplanar with the original line, then it must intersect the other also. This axiom is equivalent to the ...

If three conics pass through two given points Q and Q^', then the lines joining the other two intersections of each pair of conics P_(ij)P_(ij)^' are concurrent at a point X ...

The circular points at infinity, also called the isotropic points, are the pair of (complex) points on the line at infinity through which all circles pass. The circular ...