Sphere
Pronunciation: /sfɪər/ Explain

Figure 1: Sphere 

A sphere is all points a given distance from a
central point in 3dimensional
space.^{[2]} 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
where n is 4 or more 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
 McAdams, David E.. All Math Words Dictionary, sphere. 2nd Classroom edition 201501084799968. pg 168. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 50. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/13/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/50/mode/1up. Buy the book
More Information
 McAdams, David E.. Circle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 3/12/2009. https://www.allmathwords.org/en/c/circle.html.
Cite this article as:
McAdams, David E. Sphere. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/s/sphere.html.
Image Credits
Revision History
5/7/2019: Changed equations and expressions to new format. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/10/2018: Removed broken links, updated license, implemented new markup. (
McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (
McAdams, David E.)
12/31/2009: Added "References". (
McAdams, David E.)
12/5/2008: Changed 'equidistant' to 'a given distance'. (
McAdams, David E.)
6/7/2008: Corrected spelling. (
McAdams, David E.)
4/1/2008: Initial version. (
McAdams, David E.)