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
Science On a Sphere This work enabled MacDonald's invention to move out from the laboratory and into performance spaces. A patent was awarded to NOAA for Science On a Sphere in August 2005, with MacDonald credited as the inventor. General system architecture and configuration specifications are as follows. The carbon fiber sphere is in diameter. Other sphere sizes are possible, such as 48" and 60". Larger sizes are possible too. The 68" sphere with a single seam at the equator weighs under . The sphere is attached to the ceiling or suspension structure with a three-point suspension system to hold the sphere in place