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The mittenpunkt (also called the middlespoint) of a triangle DeltaABC is the symmedian point of the excentral triangle, i.e., the point of concurrence M of the lines from the ...

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, ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

A second-order partial differential equation of the form Hr+2Ks+Lt+M+N(rt-s^2)=0, (1) where H, K, L, M, and N are functions of x, y, z, p, and q, and r, s, t, p, and q are ...

The monster group is the highest order sporadic group M. It has group order |M| = (1) = (2) where the divisors are precisely the 15 supersingular primes (Ogg 1980). The ...

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors v ...

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The outer Soddy center (or outer Soddy point) is the center of the outer Soddy circle. It is equivalent to the isoperimetric point X_(176) (Kimberling 1994) and has ...

Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form ...

The parabiaugmented dodecahedron is a convex equilateral solid that is Johnson solid J_(60). The unit parabiaugmented dodecahedron has volume V=1/6(25+11sqrt(5)) (1) and Dehn ...