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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 surface given by the parametric equations x = asinu (1) y = asinv (2) z = asin(u+v). (3) It is a sextic surface with algebraic equation (4) The coefficients of the first ...

The singular support of a generalized function u is the complement of the largest open set on which u is smooth. Roughly speaking, it is the closed set where the distribution ...

A skew coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at angles other than right angles. Skew coordinate ...

The dual polyhedron of the small icosicosidodecahedron U_(31) and Wenninger dual W_(71).

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and ...

A submersion is a smooth map f:M->N when dimM>=dimN, given that the differential, or Jacobian, is surjective at every x in M. The basic example of a submersion is the ...

A parallel of a surface of revolution is the intersection of the surface with a plane orthogonal to the axis of revolution.