Pronunciation: /speɪs/ Explain
|Figure 1: Graph of y = 2x - 3 in Euclidean 2-space.||
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
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.
- 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. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/s/space.html.
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.)