Groups of symmetries

Groups of symmetries refer to sets of transformations that can be applied to an object without changing its essential shape. For example, if you imagine a square, you can rotate it or flip it, and it still looks the same. In mathematics, these transformations are organized into a "group," which is a way to categorize how the object can be manipulated while preserving its structure. Understanding these groups helps in various fields, from physics to art, by revealing patterns and properties of shapes and spaces.