In this lesson, the concept of the fourth dimension is explored further with a look at a 4-dimensional sphere and stereographic projections of 4-dimensional polyhedra into 3 dimensions. The S3 sphere is introduced and explained, along with the method of projecting 4-dimensional polyhedra onto a 3-dimensional space. The lesson concludes with the idea that the fourth dimension has a physical reality and is important in understanding relativistic physics, making the study of four-dimensional geometry a fascinating intersection between mathematics and physics.
This video continues a discussion of the fourth dimension, this time with a look at a 4-dimensional sphere and stereographic projections of 4-dimensional polyhedra into 3 dimensions.