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Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

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 ...

Pre-Algebra

Pre-Calculus

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

65537 is the largest known Fermat prime, and the 65537-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. The 65537-gon has so many ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...