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A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

Clausen's _4F_3 identity _4F_3(a,b,c,d; e,f,g;1)=((2a)_(|d|)(a+b)_(|d|)(2b)_(|d|))/((2a+2b)_(|d|)a_(|d|)b_(|d|)), (1) holds for a+b+c-d=1/2, e=a+b+1/2, a+f=d+1=b+g, where d a ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

A system of circles obtained by multiplying each radius in a coaxal system by a constant. The Tucker circles are a coaxaloid system (Johnson 1929, p. 277).

The coboundary polynomial chi^__G(q,t) is a bivariate graph polynomial which can be expressed in terms of the Tutte polynomial T_G(x,y) of a graph G by ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...

The companion matrix to a monic polynomial a(x)=a_0+a_1x+...+a_(n-1)x^(n-1)+x^n (1) is the n×n square matrix A=[0 0 ... 0 -a_0; 1 0 ... 0 -a_1; 0 1 ... 0 -a_2; | | ... ... |; ...

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...