Continuous symmetries in mathematics

Continuous symmetries are transformations that can be applied smoothly and gradually to a mathematical object without changing its essential structure. For example, rotating a circle by any angle or shifting a line along its length are continuous symmetries because small changes can be made without altering the object’s fundamental properties. These symmetries are described mathematically using structures called Lie groups. They play a key role in understanding physical laws and geometric shapes, showing how objects can be transformed in a seamless way while preserving their core features.