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Place 2n balls in a bag and number them 1 to 2n, then pick half of them at random. The number of different possible sums for n=1, 2, 3, ... are then 2, 5, 10, 17, 26, ... ...

The figure formed when the midpoints of the sides of a convex quadrilateral are joined in order is a parallelogram. Equivalently, the bimedians bisect each other. The area of ...

A pair of zips, each zip being half a zipper, which can be zippered up to close a surface along a curve. The concept of a zip-pair can be extremely useful in topological ...

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that |x-x_0|=r. Let x_0 be the origin. In R^1, the boundary set is then the pair of ...

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

The apodization function f(x)=1-(|x|)/a (1) which is a generalization of the one-argument triangle function. Its full width at half maximum is a. It has instrument function ...

The numbers three and four appear prominently in the game of baseball. There are three strikes for an out, three outs per half-inning (i.e., teams switch after three outs, ...