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Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

The tilde is the mark "~" placed on top of a symbol to indicate some special property. x^~ is voiced "x-tilde." The tilde symbol is commonly used to denote an operator. In ...

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

One of the four regions of the plane defined by the four possible combinations of signs (+,+), (+,-), (-,+), and (-,-) for (x,y).

A transformation consisting of rotations and translations which leaves a given arrangement unchanged.

Moving medians are implemented in the Wolfram Language as MovingMedian[data, n].