Search Results for ""

A sequence of approximations a/b to sqrt(n) can be derived by factoring a^2-nb^2=+/-1 (1) (where -1 is possible only if -1 is a quadratic residue of n). Then ...

Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...

The probability density function for Student's z-distribution is given by f_n(z)=(Gamma(n/2))/(sqrt(pi)Gamma((n-1)/2))(1+z^2)^(-n/2). (1) Now define ...

For a scalar function f over a surface parameterized by u and v, the surface integral is given by Phi = int_Sfda (1) = int_Sf(u,v)|T_uxT_v|dudv, (2) where T_u and T_v are ...

Given a Lucas sequence with parameters P and Q, discriminant D!=0, and roots a and b, the Sylvester cyclotomic numbers are Q_n=product_(r)(a-zeta^rb), (1) where ...

A second-tensor rank symmetric tensor is defined as a tensor A for which A^(mn)=A^(nm). (1) Any tensor can be written as a sum of symmetric and antisymmetric parts A^(mn) = ...

A curve investigated by Talbot which is the ellipse negative pedal curve with respect to the ellipse's center for ellipses with eccentricity e^2>1/2 (Lockwood 1967, p. 157). ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

The vector Laplacian can be generalized to yield the tensor Laplacian A_(munu;lambda)^(;lambda) = (g^(lambdakappa)A_(munu;lambda))_(;kappa) (1) = ...