Sphere
Pronunciation: /sfɪər/ ?
 Figure 1: Sphere 

A sphere is all points a given distance from a central point in
3dimensional
space.^{[1]} The distance of the surface of the sphere from the center is called the
radius.
Name  Equation 
Equation of a sphere with the center at (0,0,0)  x^{2} + y^{2} + z^{2} = r^{2} 
Equation of a sphere with the center at (x_{0},y_{0},z_{0})  (x  x_{0})^{2} + (y  y_{0})^{2} + (z  z_{0})^{2} = r^{2} 
Volume of a sphere  v = 4/3 π r^{3} 
Surface Area of a sphere  s = 4 π r^{2} 
Table 1: Equations and formulas for spheres 

The
generalization
of a sphere in
ndimensional spaces
is called a hypersphere. The equation for a
fourdimensional hypersphere is
(w  w_{0})^{2} + (x  x_{0})^{2} + (y  y_{0})^{2} + (z  z_{0})^{2} = r^{2}.
A 2 dimensional sphere is called a
circle.
Great 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
 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
 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: 20091231). http://www.archive.org/stream/elementsofconstr00noetrich#page/50/mode/1up.
 sphere. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 20110108). 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. 20090312. http://www.allmathwords.org/article.aspx?lang=en&id=Circle.
Cite this article as:
Sphere. 20091231. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/sphere.html.
Translations
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Revision History
20091231: Added "References" (
McAdams, David.)
20081205: Changed 'equidistant' to 'a given distance' (
McAdams, David.)
20080607: Corrected spelling (
McAdams, David.)
20080401: Initial version (
McAdams, David.)