Dimension

Pronunciation: /dɪˈmɛn.ʃən/ Explain

A dimension is an extension in a particular direction. A line has one dimension, since it extends in only one direction. A two dimensional space has two dimensions. An x-y graph is two dimensional. The x-axis defines one dimension and the y-axis defines another.

A dimension is not necessarily length. A dimension may also be temperature, time, mass, electrical current and others. For example, an equation may relate time and temperature: p = 2.5t where p represents temperature and t represents time. In this equation, one dimension is time and the other dimension is temperature. Albert Einstein's special theory of relativity deals with four dimensions: three dimensions are lengths making up a space, and one dimension is time. See also Dimensional Analysis.

Dimensionless

An object is said to be dimensionless if it has no dimensions. The only object in most geometries that is dimensionless is a point.

Dimensions

Number Dimensions	Manipulative	Description
0-D		A point has no dimensions.
1-D 1 dimensional		A line has one dimension.
2-D 2 dimensional		A two-variable Cartesian coordinate system has two dimensions.
2-D 2 dimensional		A rectangle has two dimensions (length and width).
3-D 3 dimensional		A three-variable Cartesian coordinate system has three dimensions.
3-D 3 dimensional		A sphere has three dimensions (length, width, and height).
4-D 4 dimensional		Euclidean space/time has four dimensions (length, width, height, and time).
Table 1: Dimensions

References

1. McAdams, David E.. All Math Words Dictionary, dimension. 2nd Classroom edition 20150108-4799968. pg 61. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

• McAdams, David E.. Space. allmathwords.org. Life is a Story Problem LLC. 3/12/2009. http://www.allmathwords.org/en/s/space.html.
• Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.

Cite this article as:

McAdams, David E. Dimension. 4/19/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/dimension.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

4/19/2019: Updated equations and expressions to the new format (McAdams, David E.)
1/5/2019: Added vocabulary links, corrected order of dimensions in table. Corrected size of Geogebra Apps. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/23/2010: Added "References". (McAdams, David E.)
11/22/2009: Added manipulatives. (McAdams, David E.)
7/11/2008: Added table of dimensions. (McAdams, David E.)
7/7/2008: Corrected spelling errors. (McAdams, David E.)
5/7/2008: Added discussion of non-length dimensions. (McAdams, David E.)
3/10/2008: Initial version. (McAdams, David E.)
1/28/2008: Added link to Albert Einstein biography. (McAdams, David E.)