Relationship Between Symmetry in Nature and Mathematics.

Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that sometimes 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 its structure.

Symmetries are immensely important because every symmetry can be expressed as a conservation law. This effect, due to Noether’s Theorem, allows you a very general and elegant way to discover fundamental laws of the universe.

There are four types of symmetry: Translation, rotation, reflection, and glide relation.

Note: Noether’s Theorem: states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. This theorem only applies to continuous and smooth symmetries over physical space.

Most of this information was obtained from the ever generous Wikipedia. Always expanding our mind.