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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 ...

Abstract Algebra

A q-series is series involving coefficients of the form (a;q)_n = product_(k=0)^(n-1)(1-aq^k) (1) = product_(k=0)^(infty)((1-aq^k))/((1-aq^(k+n))) (2) = ...

The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwārizmī about algebraic methods. In modern usage, algebra has several meanings. One use of the ...

Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

A Diophantine equation is an equation in which only integer solutions are allowed. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary ...

An Egyptian fraction is a sum of positive (usually) distinct unit fractions. The famous Rhind papyrus, dated to around 1650 BC contains a table of representations of 2/n as ...

There are many mathematical and recreational problems related to folding. Origami, the Japanese art of paper folding, is one well-known example. It is possible to make a ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...