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The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted rho_A), opposite side of length a and angle A, area Delta, and semiperimeter s. Then r_1 = ...

Let a straight line AB be divided internally at C and externally at D in the same ratio, so that (AC)/(CB)=-(AD)/(DB). Then AB is said to be divided harmonically at C and D ...

"The" Jacobi identity is a relationship [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0,, (1) between three elements A, B, and C, where [A,B] is the commutator. The elements of a Lie algebra ...

A graph Gamma is locally Petersen if, for each point t of Gamma, the graph induced by Gamma on all points adjacent to t (i.e., the neighborhood graph) is isomorphic to the ...

A number which is simultaneously octagonal and pentagonal. Let O_n denote the nth octagonal number and P_m the mth pentagonal number, then a number which is both octagonal ...

A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a ...

A figurate number which is constructed as a centered cube with a square pyramid appended to each face, RhoDod_n = CCub_n+6P_(n-1)^((4)) (1) = (2n-1)(2n^2-2n+1), (2) where ...

The small dodecahemidodecahedron is the uniform polyhedron with Maeder index 51 (Maeder 1997), Wenninger index 91 (Wenninger 1989), Coxeter index 65 (Coxeter et al. 1954), ...

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...

The Barth sextic is a sextic surface in complex three-dimensional projective space having the maximum possible number of ordinary double points, namely 65. The surface was ...