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Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).

The plane through the midpoint of a line segment and perpendicular to that segment, also called a mediating plane. The term "mediator" was introduced by J. Neuberg ...

A transformation characterized by an invariant line and a scale factor (one-way stretch) or two invariant lines and corresponding scale factors (two-way stretch).

Given a triangle DeltaABC and the excentral triangle DeltaJ_AJ_BJ_C, define the A^'-vertex of the hexyl triangle as the point in which the perpendicular to AB through the ...

Inscribe two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 in a reference triangle DeltaABC such that A = ∠AB_1C_1=∠AC_2B_2 (1) B = ∠BC_1A_1=∠BA_2C_2 (2) C = ∠CA_1B_1=∠CB_2A_2. ...

A binary Hamming code H_r of length n=2^r-1 (with r>=2) is a linear code with parity-check matrix H whose columns consist of all nonzero binary vectors of length r, each used ...

Consider decomposition the factorial n! into multiplicative factors p_k^(b_k) arranged in nondecreasing order. For example, 4! = 3·2^3 (1) = 2·3·4 (2) = 2·2·2·3 (3) and 5! = ...

The theory of point sets and sequences having a uniform distribution. Uniform distribution theory is important in modeling and simulation, and especially in so-called Monte ...

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 ...

The symbol RadicalBox[x, n] used to indicate a root is called a radical, or sometimes a surd. The expression RadicalBox[x, n] is therefore read "x radical n," or "the nth ...