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 ?
At night one could imagine that the stars might sing The forgotten music of the spheres.
But while I accept Hazlewood's contention and accept while Oldfield nodded in the direction of the West Coast experimenters, he bowed towards 19th and 20th Century harmonic symphonists and as his most recent opus, Music Of The Spheres, shows still does.
I'm glad it's changed its doubting tune back to / the music of the spheres, of sorts; / especially now that I again see you / walking in the garden as you used to do / long, long ago.
A Rhythm, a Tick The music of the spheres becomes the metre and beat of your digits.
Music Of The Spheres draws on the idea that all celestial bodies have an inner music inaudible to the human ear.
The concert concluded with The Blue Danube (with The Radetzky March as a traditional clap-along encore), and we heard famous Strauss family compositions such as Wine, Women and Song, the Thunder and Lightning Polka, Tales from the Vienna Woods and Music of the Spheres.
Top-notch chamber group London Sinfonietta play Messiaen's Quartet for the End of Time and the final Candlelight Concert has the superb vocal group I Fagiolini singing Music of the Spheres.
Well that is certainly what the Whitneys (who thought in terms of the music of the spheres, atomic particles, and "liquid architecture") wanted.
Obviously, some artistic license would need to be taken, but what a challenge to create true music of the spheres.
Though captured in sound, the transcendent immateriality of these works connects, albeit circuitously, with concepts such as music of the spheres (pp.
Brown is currently riding high on the critical and commercial success of his third solo album - Music of the Spheres, although it's been a real battle for him to get there, ever since the Stone Roses ended unhappily in 1996 with the resignation of guitarist John Squire.
His latest album Music Of The Spheres - his best yet - was as surprising in musical terms as the prospect of Darius winning Pop Idol.