The Fourth Dimension Continued
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Lesson Summary:
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.
Lesson Description:
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.
Questions answered by this video:
- What is the 4th dimension?
- How can you visualize the fourth dimension?
- What does a 4-dimensional sphere look like?
- What is a simplex?
- What is a hypercube?
- What is a 24-cell, 120-cell, and 600-cell?
- What do 4-dimensional polyhedra look like when stereographically projected in 3 dimensions?
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Staff Review
This video uses analogy similar to the previous video in this series, but now it looks at a 4-dimensional sphere, or S3 sphere. Also, the other 4-dimensional polyhedra that have already been analyzed are viewed using stereographic projections onto 3-space. The resulting images are quite spectacular.
