[Math Lair] Symmetry

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In mathematics, a figure possessing symmetry can be subjected to certain operations which leave the whole unchanged.

The letters A and B have bilateral symmetry by vertical and horizontal reflection respectively. The letter Z is symmetrical for a rotation through 180°.

For mathematical convenience the identity operation, leaving the figure unchanged, is included in the list of symmetrical operations, so that even a completely irregular figure has this symmetry.

Symmetry can also be used in a broader sense in other branches of mathematics to describe a property that does not change under certain types of transformations. For example, the equation x² + y² = 25 could be considered symmetric with respect to x and y, since exchanging x and y in the equation produces the same equation.