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Sphere Books was a British paperback publisher of the 1960s - 1980s.
Sphere is the name of a book written by Michael Crichton, which
was subsequently turned into a movie by the same name.
A sphere is, roughly speaking, a ball-shaped object. In mathematics, a sphere is consisting only of a surface and is
therefore hollow.
In non-mathematical usage a sphere is often considered to be solid (which mathematicians call ball).
More precisely, a sphere is the set of points in 3-dimensional Euclidean space which are at distance r from a fixed point of that space, where r is a
positive real number called the radius of the sphere. The
special case of r = 1 is called a unit sphere.
In coordinate geometry, a sphere with center
(x0, y0, z0) and radius r is the set of all points
(x,y,z) such that
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The points on the sphere with radius r and center at the origin can be parametrized via
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(see trigonometric functions and spherical coordinates).
A sphere of any radius centered at the origin is described by the following differential equation:
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The surface area of a sphere of radius r is
4πr2, and its inclosed volume is
4πr3/3. The sphere has the smallest surface area among all surfaces enclosing a given volume and it
encloses the largest volume among all closed surfaces with a given surface area. For this reason, the sphere appears in nature:
for instance bubbles and water drops (in the absence of gravity) are spheres because
the surface tension tries to minimize surface area.
The circumscribed cylinder for a given sphere has a volume which is 3/2 times
the volume of the sphere, and also a surface area which is 3/2 times the surface area of the sphere. This fact, along with the
volume and surface formulas given above, was already known to Archimedes.
A sphere can also be defined as the surface formed by rotating a circle about its
diameter. If the circle is replaced by an ellipse, the shape becomes a spheroid.
Spheres can be generalized to other dimensions. For any natural number n, an n-sphere is the set of points in
(n+1)-dimensional Euclidean space which are at distance r from a fixed point of that space, where r
is, as before, a positive real number. A 2-sphere is therefore an ordinary sphere, while a 1-sphere is a circle and a 0-sphere is a pair of points. The n-sphere of unit radius centered at the origin is
denoted Sn and is often referred to as "the" n-sphere.
An n-sphere is an example of a compact n-manifold.
See also
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