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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 ...

Ball tetrahedron picking is the selection of quadruples of points (corresponding to vertices of a general tetrahedron) randomly placed inside a ball. n random tetrahedra can ...

In the American system, one billion equals 10^9=1000000000. In the French and German systems, one billion equals 10^(12). In recent years, the "American" system has become ...

How far can a stack of n books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_n for n books (in terms of ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

The finite simple groups of Lie-type. They include four families of linear simple groups: PSL(n,q) (the projective special linear group), PSU(n,q) (the projective special ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

The Conway-Smith graph is a distance-transitive graph on 63 vertices having intersection array {10,6,4,1;1,2,6,10} (Hall 1980). It is also distance-transitive. It is denoted ...

The Golay code is a perfect linear error-correcting code. There are two essentially distinct versions of the Golay code: a binary version and a ternary version. The binary ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...