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.

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Manipulative 1: Dilation of a triangle.


  1. invariant. WordNet. Princeton University. (Accessed: 2011-01-08).
  2. Glenn, Oliver E.. A Treatise on the Theory of Invariants. Ginn and Company, 1915. (Accessed: 2010-03-02).
  3. Lin I-hsiung. Geometric Linear Algebra, vol 2 pg 194-205. World Scientific Publishing Company, May 6, 2008.
  4. A. B. Kharazishvili. Transformation Groups and Invariant Measures: Set-Theoretical Aspects. World Scientific Publishing Company, September 1998.

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Cite this article as:

Invariant. 2009-09-16. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-03-02: Added "References", clarified wording (McAdams, David.)
2008-09-16: Initial Version (McAdams, David.)

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