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The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

An elliptic fixed point of a differential equation is a fixed point for which the stability matrix has purely imaginary eigenvalues lambda_+/-=+/-iomega (for omega>0). An ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

The elliptic hyperboloid is the generalization of the hyperboloid to three distinct semimajor axes. The elliptic hyperboloid of one sheet is a ruled surface and has Cartesian ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...

The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

A quadratic surface which has elliptical cross section. The elliptic paraboloid of height h, semimajor axis a, and semiminor axis b can be specified parametrically by x = ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

Elliptic rational functions R_n(xi,x) are a special class of rational functions that have nice properties for approximating other functions over the interval x in [-1,1]. In ...