Space
Pronunciation: /speɪs/ Explain
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Figure 1: Graph of
y = 2x - 3 in Euclidean
2-space. |
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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 2-space.
An x-y graph
exists in Euclidean 2-space. 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 2-space refers to the fact that this
space has two dimensions: length and width.
The term n-space is used to define a space
with n dimensions. For example, a
2-space
is a space with 2 dimensions. A
3-space is a space with 3
dimensions.
Some spaces that are often used in mathematics are:
- Euclidean n-space: A space following the rules of Euclidean geometry
with n dimensions.
- Minkowski space: Euclidean 3-space 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.
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References
- McAdams, David E.. All Math Words Dictionary, space. 2nd Classroom edition 20150108-4799968. 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. https://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 n-space. (
McAdams, David E.)
8/20/2007: Initial version. (
McAdams, David E.)