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(x^2)/(a^2-lambda)+(y^2)/(b^2-lambda)=z-lambda (1) (x^2)/(a^2-mu)+(y^2)/(b^2-mu)=z-mu (2) (x^2)/(a^2-nu)+(y^2)/(b^2-nu)=z-nu, (3) where lambda in (-infty,b^2), mu in ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

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 ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

A line making equal angles with the edges of a trihedron is called an isoclinal line of the trihedron.

The four planes determined by the four altitudes of a tetrahedron and the orthocenters of the corresponding faces pass through the Monge point of the tetrahedron.