Space
Pronunciation: /speɪs/ Explain

Figure 1: Graph of
y = 2x  3 in Euclidean
2space. 

A mathematical space is a set of properties
governing the interaction of objects contained in the space.
A common example of a space is Euclidean 2space.
An xy graph
exists in Euclidean 2space. The word Euclidean means that objects
have the properties associated with
Euclidean geometry,
most importantly the fifth postulate which controls the intersection of lines.
The 2 in 2space refers to the fact that this
space has two dimensions: length and width.
The term nspace is used to define a space
with n dimensions. For example, a
2space
is a space with 2 dimensions. A
3space is a space with 3
dimensions.
Some spaces that are often used in mathematics are:
 Euclidean nspace: A space following the rules of Euclidean geometry
with n dimensions.
 Minkowski space: Euclidean 3space with time as a fourth dimension.
This space was used by Albert Einstein for his theory of Special Relativity.
 Hyperbolic geometry: The difference between Euclidean geometry and Hyperbolic
geometry is that, given a line and a point not on the line, in Euclidean geometry there
is a unique line passing through the point that are parallel to the given line. In
Hyperbolic geometry, there are infinite lines passing through the point that are
parallel to the given line.
One attribute that a space can have is a metric space. In
a metric space, location can be measured from the origin, and the distance between one
location and another can be measured.

References
 McAdams, David E.. All Math Words Dictionary, space. 2nd Classroom edition 201501084799968. pg 168. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
 Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.
Cite this article as:
McAdams, David E. Space. 5/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/space.html.
Image Credits
Revision History
5/13/2019: 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.)
6/7/2008: Corrected spelling. (
McAdams, David E.)
3/11/2008: Corrected formatting. (
McAdams, David E.)
3/10/2008: Added reference to nspace. (
McAdams, David E.)
8/20/2007: Initial version. (
McAdams, David E.)