## Symmetries & Transformations

Historically, the idea of beauty has often been tied to *symmetry*, considered the fundamental characteristic of a sense of harmonious proportion and balance.

Over time, humans have imitated nature’s symmetries in various artistic and creative expressions, whether visual art, architecture, music, dance, literature, or technological advancement.

Besides defining the perception of what is beautiful and pleasant to our senses, symmetry also plays a complex, deeper role: it lies at the very foundations of our universe, explaining some of the most fundamental laws of physics.

In *geometry*, an object is symmetric if it looks the same, even after applying a certain *rigid transformation*. Such a transformation converts one geometric figure into another without changing its size or shape: we can move it, turn it, or flip it over, but we cannot stretch, bend, or otherwise deform it.

Symmetry also refers to a much wider concept in physics and mathematics: *immunity to change*, under transformations of very different natures, including space and even time shifting.

Conservation laws are fundamental in physics as they describe which processes can or cannot occur in nature. Each conservation law is the consequence of a symmetry in nature. And due to their symmetries, some of these laws are said to be exact: they have never been proven to be violated.

Symmetry is a fundamental and familiar concept whose applicability can go far beyond our perception. But no matter where it occurs, it remains intimately related to our intuition: as a manifestation of harmony, balance, and beauty.