Higher-dimensional spheres

Higher-dimensional spheres, or n-spheres, are generalizations of the familiar 2-sphere (a normal sphere like Earth's surface) into more than three dimensions. They are mathematical shapes consisting of all points that are a fixed distance from a central point in an (n+1)-dimensional space. For example, a 3-sphere exists in four-dimensional space and is the set of points equally distant from a center in that space. While we cannot visualize these directly, they help in understanding complex systems, mathematical theories, and physics by extending the familiar concept of a sphere into higher dimensions.