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A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...

The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...

Divide a set of data into two groups (high and low) of equal size at the statistical median if there is an even number of data points, or two groups consisting of points on ...

The direct sum of modules A and B is the module A direct sum B={a direct sum b|a in A,b in B}, (1) where all algebraic operations are defined componentwise. In particular, ...

One of the set of symbols C_i, C_s, C_1, C_2, C_3, C_4, C_5, C_6, C_7, C_8, C_(2h), C_(3h), C_(4h), C_(5h), C_(6h), C_(2v), C_(3v), C_(4v), C_(5v), C_(6v), C_(inftyv), D_2, ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

The series z=ln(e^xe^y) (1) for noncommuting variables x and y. The first few terms are z_1 = x+y (2) z_2 = 1/2(xy-yx) (3) z_3 = 1/(12)(x^2y+xy^2-2xyx+y^2x+yx^2-2yxy) (4) z_4 ...

Let the circles c_2 and c_3^' used in the construction of the Brocard points which are tangent to A_2A_3 at A_2 and A_3, respectively, meet again at D_A. The points D_AD_BD_C ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...