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The following other wikis use this file: Usage on ar.wikipedia.org كرة; Usage on bar.wikipedia.org Archimedes; Usage on cy.wikipedia.org Silindr
A sphere (from Greek σφαῖρα, sphaîra) [1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [2]
Sphere packing finds practical application in the stacking of cannonballs.. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space.
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.
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 : (), = ….
We assume that is well behaved and that we can reverse the order of integration. Also, recall that flow is normal to the unit area of the cell. Now, since in one dimension , we can apply the divergence theorem, i.e. =, and substitute for the volume integral of the divergence with the values of () evaluated at the cell surface (edges / and + /) of the finite volume as follows:
The 3-dimensional surface volume of a 3-sphere of radius r is = while the 4-dimensional hypervolume (the content of the 4-dimensional region, or ball, bounded by the 3-sphere) is
Poincaré asks us to imagine a sphere of radius R.The temperature of the sphere decreases from its maximum at the center to absolute zero at its extremity such that a body’s temperature at a distance r from the center is proportional to .