Sphere

sphere, in geometry, the three-dimensional analogue of a circle. 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.

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sphere

In geometry, the set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters. The components and properties of a sphere are analogous to those of a circle. A diameter is any line segment connecting two points of a sphere and passing through its centre. The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre. A meridian is any great circle passing through a point designated a pole. A geodesic, the shortest distance between any two points on a sphere, is an arc of the great circle through the two points. The formula for determining a sphere's surface area is 4πr²; its volume is determined by (⁴⁄₃)πr³. The study of spheres is basic to terrestrial geography and is one of the principal areas of Euclidean geometry and elliptic geometry.

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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)

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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 equationx² + y² + z²=1.

The set of points in a metric space whose distance from a fixed point is constant.

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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.

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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.