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Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

Given two intersecting lines or line segments, the amount of rotation about the point of intersection (the vertex) required to bring one into correspondence with the other is ...

The Kakeya needle problems asks for the plane figure of least area in which a line segment of width 1 can be freely rotated (where translation of the segment is also ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

For a real positive t, the Riemann-Siegel Z function is defined by Z(t)=e^(itheta(t))zeta(1/2+it). (1) This function is sometimes also called the Hardy function or Hardy ...

The Schröder number S_n is the number of lattice paths in the Cartesian plane that start at (0, 0), end at (n,n), contain no points above the line y=x, and are composed only ...

For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...