symmetry math definition
Symmetry in mathematics Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that something does not change under a set of transformations. Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure. This occurs in many cases; for example, if X is a set with no additional structure, a symmetry is a bijective map from the set to itself, giving rise to permutation groups.