The circle in two dimensions and the sphere in three are just two members of an infinite family of hyper-surfaces. By analogy with the circle in the plane and the sphere in three-space , we can consider hyper-spheres in higher dimensional spaces. In particular, we will consider the 3-sphere which can be embedded in but can also be envisaged as a non-Euclidean manifold in .

Continue reading ‘The 3-sphere: Extrinsic and Intrinsic Forms’