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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]
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.
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 : (), = ….
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.
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
On 7 April 1795, the metric system was formally defined in French law using six units. Three of these are related to volume: the stère (1 m 3) for volume of firewood; the litre (1 dm 3) for volumes of liquid; and the gramme, for mass—defined as the mass of one cubic centimetre of water at the temperature of melting ice. [10]
MUNICH (Reuters) -President Volodymyr Zelenskiy said on Saturday a draft minerals deal with Washington did not contain the security provisions that Kyiv needed and three sources said the United ...
Visualization of the whole observable universe.The inner blue ring indicates the approximate size of the Hubble volume. In cosmology, a Hubble volume (named for the astronomer Edwin Hubble) or Hubble sphere, subluminal sphere, causal sphere and sphere of causality is a spherical region of the observable universe surrounding an observer beyond which objects recede from that observer at a rate ...