Invariant
Pronunciation: /ɪnˈvɛər i ənt/ ?
Properties of a mathematical object undergoing a
transformation
that are unchanged by the transformation are called
invariant. Manipulative 1 shows a
dilation
of a triangle.
Properties of the triangle that are invariant under dilation are the measures of the angles, and the
ratios between the measures of the sides. Properties of the triangle that are not invariant
are the lengths of the sides and the area of the triangle.

Manipulative 1: Dilation of a triangle.

References
 invariant. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 20110108). http://wordnetweb.princeton.edu/perl/webwn?s=invariant&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
 Glenn, Oliver E.. A Treatise on the Theory of Invariants. Ginn and Company, 1915. (Accessed: 20100302). http://www.archive.org/stream/treatiseontheory00glenrich#page/n14/mode/1up/search/invariant.
 Lin Ihsiung. Geometric Linear Algebra, vol 2 pg 194205. World Scientific Publishing Company, May 6, 2008.
 A. B. Kharazishvili. Transformation Groups and Invariant Measures: SetTheoretical Aspects. World Scientific Publishing Company, September 1998.
Printed Resources
Cite this article as:
Invariant. 20090916. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/invariant.html.
Translations
Image Credits
Revision History
20100302: Added "References", clarified wording (
McAdams, David.)
20080916: Initial Version (
McAdams, David.)