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Perspective is the art and mathematics of realistically depicting three-dimensional objects in a two-dimensional plane, sometimes called centric or natural perspective to ...

A sequence {a_n}_(n=1)^N forms a (binary) heap if it satisfies a_(|_j/2_|)<=a_j for 2<=j<=N, where |_x_| is the floor function, which is equivalent to a_i<a_(2i) and ...

The Champernowne constant has decimal expansion C=0.1234567891011... (OEIS A033307). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

Define the packing density eta of a packing of spheres to be the fraction of a volume filled by the spheres. In three dimensions, there are three periodic packings for ...

Given an n-dimensional vector x=[x_1; x_2; |; x_n], (1) a general vector norm |x|, sometimes written with a double bar as ||x||, is a nonnegative norm defined such that 1. ...

A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0. For example, there are 10 singular 2×2 (0,1)-matrices: [0 0; 0 0],[0 0; 0 ...

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...