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A surface of revolution defined by Kepler. It consists of less than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

The nth raw moment mu_n^' (i.e., moment about zero) of a distribution P(x) is defined by mu_n^'=<x^n>, (1) where <f(x)>={sumf(x)P(x) discrete distribution; intf(x)P(x)dx ...

The geometric centroid of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as x^_ = ...

The volume of a polyhedron composed of N triangular faces with vertices (a_i,b_i,c_i) can be computed using the curl theorem as V=1/6sum_(i=1)^Na_i·n_i, where the normal n_i ...

Russian roulette is a game of chance in which one or more of the six chambers of a revolver are filled with cartridges, the chamber is rotated at random, and the gun is ...

A sequence is an ordered set of mathematical objects. Sequences of object are most commonly denoted using braces. For example, the symbol {2n}_(n=1)^infty denotes the ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...