3-sphere two 3-balls. This construction is analogous to a construction of a 2-sphere, performed by gluing the boundaries of a pair of disks. A disk is a 2-ball, and the boundary of a disk is a circle (a 1-sphere). Let a pair of disks be of the same diameter. Superpose them and glue corresponding points on their boundaries. Again one may think of the third dimension as temperature. Likewise, we may inflate the 2-sphere, moving the pair of disks to become the northern and southern hemispheres. After removing a single point from the 2-sphere, what remains is homeomorphic to the Euclidean
Inversion in a sphere in this article are dependent on three simple ideas: (See fig 1) (See fig 2) (See fig 3) Note 4: Generally, the inverse of a line is a circle through the centre of reference. Note 5: Generally, the inverse of a plane is a sphere through the centre of reference. (See fig 4) (See fig 5) Note 6: Generally the inverse of a sphere is a sphere (Cf Figs 3, 4, 5) Note 7: Generally the inverse of a circle is a circle. Inversion in a sphere In geometry, inversion in a sphere is a transformation of Euclidean space that