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The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a number of subtle mathematical relationships. For instance, the florets in the head of a ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

A Barker code is a string of digits a_i=+/-1 of length l>=2 such that |sum_(i=1)^(l-k)a_ia_(i+k)|<=1 for all 1<=k<l. Barker codes are used for pulse compression of radar ...

A board is a subset of the polygons determined by a number of (usually regularly spaced and oriented) lines. These polygons form the spaces on which "pieces" can be placed ...

A uniform distribution of points on the circumference of a circle can be obtained by picking a random real number between 0 and 2pi. Picking random points on a circle is ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...