Search Results for ""

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

Consider a game where everyone in a classroom picks a number between 0 and 100. The person closest to half the average wins. Obviously, picking a number over 50 would be ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

The order n T-polyomino consists of a vertical line of n-3 squares capped by a horizontal line of three squares centered on the line.

A quantitative measure of the simplicity of a geometric construction which reduces geometric constructions to five steps. It was devised by È. Lemoine. S_1 Place a ...

A collection of subsets of a topological space that is contained in a basis of the topology and can be completed to a basis when adding all finite intersections of the ...