Definition: A symmetry is a correspondence of form under some transformation, often on opposite sides of a dividing line or plane or about a center or an axis. This correspondence may be a congruence, identity or equivalence..
The idea of symmetry is intimately bound up with harmony and balance; rhythm and repetition - essential ingredients of beauty
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http://standards.nctm.org/document/eexamples/chap6/6.4/index.htm
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