Unit sphere ($S^n$)

A unit sphere is a mathematical concept that refers to the set of points in a given space that are at a unit distance (usually 1) from a central point, called the center of the sphere. In different dimensions, the unit sphere can be defined as follows: 1. **In 2 dimensions (2D)**: The unit sphere is a circle of radius 1 centered at the origin (0, 0) in the Cartesian plane.