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Consider the linear subspace of the n-dimensional Euclidean space R n that is spanned by a collection of linearly independent vectors , …,. To find the volume element of the subspace, it is useful to know the fact from linear algebra that the volume of the parallelepiped spanned by the is the square root of the determinant of the Gramian matrix of the : (), = ….
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If f(x, y, z) = 0 and g(x, y, z) = 0 are the equations of two distinct spheres then (,,) + (,,) = is also the equation of a sphere for arbitrary values of the parameters s and t. The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition a sphere is allowed to be a ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 27 February 2025. American multinational home improvement supplies retailing company The Home Depot, Inc. A Home Depot in Onalaska, Wisconsin Company type Public Traded as NYSE: HD DJIA component S&P 100 component S&P 500 component Industry Retail (home improvement) Founded February 6, 1978 ; 47 years ...
In coordinates, a 3-sphere with center (C 0, C 1, C 2, C 3) and radius r is the set of all points (x 0, x 1, x 2, x 3) in real, 4-dimensional space (R 4) such that = = + + + =. ...
A Hoberman Sphere at the National Museum of American History Second largest Hoberman sphere in the world, undergoing maintenance at Liberty Science Center. A Hoberman sphere is a kinetic structure patented by Chuck Hoberman that resembles a geodesic dome, but is capable of folding down to a fraction of its normal size by the scissor-like action of its joints.
Three Spheres II is a lithograph print by the Dutch artist M. C. Escher first printed in April 1946.. As the title implies, it depicts three spheres resting on a flat surface. ...