Pronunciation: /ɪnˈvɛər.i.ənt/ Explain
Properties of a mathematical object undergoing a
that are unchanged by the transformation are called
invariant. Manipulative 1 shows a
of a triangle.
Properties of a 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.
Click on points and drag them to change the figure. |
Which of the following never change for dilation: Angle measure, length of side, ratio of sides, are of the triangle?
|Manipulative 1 - Invariant Created with GeoGebra.|
- McAdams, David E.. All Math Words Dictionary, invariant. 2nd Classroom edition 20150108-4799968. pg 101. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Glenn, Oliver E.. A Treatise on the Theory of Invariants. www.archive.org. Ginn and Company. 1915. Last Accessed 8/7/2018. http://www.archive.org/stream/treatiseontheory00glenrich#page/n14/mode/1up/search/invariant. Buy the book
- Lin I-hsiung. Geometric Linear Algebra. vol 2 pg 194-205. World Scientific Publishing Company. May 6, 2008. Last Accessed 8/7/2018. Buy the book
- A. B. Kharazishvili. Transformation Groups and Invariant Measures: Set-Theoretical Aspects. World Scientific Publishing Company. September 1998. Last Accessed 8/7/2018. Buy the book
Cite this article as:
McAdams, David E. Invariant. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/invariant.html.
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
3/2/2010: Added "References", clarified wording. (McAdams, David E.)
9/16/2008: Initial Version. (McAdams, David E.)