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Klee's identity is the binomial sum sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n), where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following ...

A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy |l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 ...

The crossed trough is the surface z=x^2y^2. (1) The coefficients of its first fundamental form are E = 1+4x^2y^4 (2) F = 4x^3y^3 (3) G = 1+4x^4y^2 (4) and of the second ...

sum_(n=0)^(N-1)e^(inx) = (1-e^(iNx))/(1-e^(ix)) (1) = (-e^(iNx/2)(e^(-iNx/2)-e^(iNx/2)))/(-e^(ix/2)(e^(-ix/2)-e^(ix/2))) (2) = (sin(1/2Nx))/(sin(1/2x))e^(ix(N-1)/2), (3) ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

Gieseking's constant is defined by G = int_0^(2pi/3)ln(2cos(1/2x))dx (1) = Cl_2(1/3pi) (2) = (3sqrt(3))/4[1-sum_(k=0)^(infty)1/((3k+2)^2)+sum_(k=1)^(infty)1/((3k+1)^2)] (3) = ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

A 4-hyperboloid has negative curvature, with R^2=x^2+y^2+z^2-w^2 (1) 2x(dx)/(dw)+2y(dy)/(dw)+2z(dz)/(dw)-2w=0. (2) Since r=xx^^+yy^^+zz^^, (3) it follows that ...