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The quantity ps-rq obtained by letting x = pX+qY (1) y = rX+sY (2) in ax^2+2bxy+cy^2 (3) so that A = ap^2+2bpr+cr^2 (4) B = apq+b(ps+qr)+crs (5) C = aq^2+2bqs+cs^2 (6) and ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

The minimal polynomial S_n(x) whose roots are sums and differences of the square roots of the first n primes, ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...