Sphere

Pronunciation: /sfɪər/ ?

Sphere
Figure 1: Sphere

A sphere is all points a given distance from a central point in 3-dimensional space.[1] The distance of the surface of the sphere from the center is called the radius.

NameEquation
Equation of a sphere with the center at (0,0,0)x2 + y2 + z2 = r2
Equation of a sphere with the center at (x0,y0,z0)(x - x0)2 + (y - y0)2 + (z - z0)2 = r2
Volume of a spherev = 4/3 π r3
Surface Area of a spheres = 4 π r2
Table 1: Equations and formulas for spheres

The generalization of a sphere in n-dimensional spaces is called a hypersphere. The equation for a four-dimensional hypersphere is (w - w0)2 + (x - x0)2 + (y - y0)2 + (z - z0)2 = r2. A 2 dimensional sphere is called a circle.

Great Circle

Sphere showing a great circle and a small circle.
Figure 2: Sphere showing a great circle and a small circle.

A great circle is a circle on a sphere with the same diameter as the sphere. Circles on a sphere that are not great circles are called small circles. For more information see Great Circle.

Hemisphere

Hemisphere: Half of a sphere
Figure 3: Hemisphere

A hemisphere is exactly half of a sphere. A hemisphere can be created using any plane that contains a diameter of the circle.

References

  1. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pg 50. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-31). http://www.archive.org/stream/elementsofconstr00noetrich#page/50/mode/1up.
  2. sphere. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=sphere&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

More Information

  • McAdams, David. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Circle.

Cite this article as:


Sphere. 2009-12-31. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/sphere.html.

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Revision History


2009-12-31: Added "References" (McAdams, David.)
2008-12-05: Changed 'equidistant' to 'a given distance' (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-04-01: Initial version (McAdams, David.)

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