sphere

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sphere,

in geometry, the three-dimensional analogue of a circlecircle,
closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
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. The term is applied to the spherical surface, every point of which is the same distance (the radius) from a certain fixed point (the center), and also to the volume enclosed by such a surface. The curve formed by a plane cutting a sphere is a circle. If the plane goes through the center of the sphere, the circle is called a great circle of the sphere. It is the largest circle that can be drawn upon the sphere, and all great circles of the same or equal spheres are of equal size. The shortest distance between two points on a spherical surface, measured on the surface, is the distance along the great circle through those points. A plane cutting a sphere in a great circle divides the sphere into two equal segments called hemispheres. The diameter of a sphere is the diameter of one of its great circles. The formula for the area of the surface of a sphere is S=4πr2, and for the volume it is V= 4-3 πr3, where r is the radius of the sphere. Spherical geometry and spherical trigonometry are methods of determining magnitudes and figures on a spherical surface.

Sphere

 

a closed surface all points of which are equally distant from a fixed point called the center of the sphere. A line segment joining the center and any of the points of a sphere is called the radius of the sphere. The term “radius” is also applied to the length of the segment. The area of a sphere is S = 4πR2, where R is the sphere’s radius.

The portion of space bounded by a sphere and containing its center is also called a sphere. The volume of such a portion of space is V = 4π/R3/3.

From the standpoint of analytic geometry, a sphere is a central quadric surface whose equation in rectangular coordinates has the form

(x – a)2 + (y – b)2 + (z – c)2 = R2

where a, b, and c are the coordinates of the center of the sphere.


Sphere

 

the geometric solid generated by revolving a circle about its diameter. A sphere is the locus of points in space at a distance not greater than a specified distance R from a fixed point. The fixed point is called the center of the sphere, and R is known as the sphere’s radius. The volume of a sphere is V = 4πR3/3. The surface of a sphere is also called a sphere; its area is S = 4πR2.

sphere

[sfir]
(mathematics)
The set of all points in a euclidean space which are a fixed common distance from some given point; in Euclidean three-dimensional space the Riemann sphere consists of all points (x,y,z) which satisfy the equation x 2 + y 2 + z 2=1.
The set of points in a metric space whose distance from a fixed point is constant.

sphere

1. Maths
a. a three-dimensional closed surface such that every point on the surface is equidistant from a given point, the centre
b. the solid figure bounded by this surface or the space enclosed by it. Equation: (x--a)2 + (y--b)2 + (z--c)2 = r2, where r is the radius and (a, b, c) are the coordinates of the centre; surface area: 4πr2; volume: 4πr3/3
2. the night sky considered as a vaulted roof; firmament
3. any heavenly object such as a planet, natural satellite, or star
4. (in the Ptolemaic or Copernican systems of astronomy) one of a series of revolving hollow globes, arranged concentrically, on whose transparent surfaces the sun (or in the Copernican system the earth), the moon, the planets, and fixed stars were thought to be set, revolving around the earth (or in the Copernican system the sun)
References in periodicals archive ?
Hence the manifold represented by (13) is foliated by 2-spheres of radius greater than [alpha] = 2m--the spacetime has a hole in its centre
In fact, as we have just seen, the line-element (16) only corresponds to the exterior Schwarzschild solution, which is a manifold foliated by 2-spheres with radial coordinate R > [alpha].
The invalid conventional assumptions that 0 < r < [alpha] and that r is a radius of sorts in the gravitational field lead to the incorrect conclusion that r=[alpha] is a 2-sphere in the gravitational field of the point-mass.