Transformation groups

Transformation groups refer to a mathematical concept where a set of transformations, such as rotations or translations, can be systematically studied. These transformations can change shapes or positions of objects in a space while preserving certain properties. In essence, a transformation group is a way to understand how objects can be manipulated or altered in a structured manner. It has applications across various fields, including physics, robotics, and even art, as it provides insights into symmetry and conservation laws, helping us comprehend the underlying patterns in both mathematical structures and physical phenomena.