# **SEE-Math**

## Texas A&M University

# **Public Lecture: 4D Geometry**

## Philip Yasskin

The main part of this presentation was a 10 minute movie entitled "Hypercube" by Thomas Banchoff of Brown University. The first half of the movie shows rotations of a 4 dimensional cube while the second half shows the 3 dimensional slices through the 4 dimensional cube.
This is preceded by a discussion of the definition of a 4 dimensional cube as shown in the diagrams:

The cube in each dimension is constructed by drawing 2 cubes of the previous dimension (blue and red) and connecting corresponding vertices (magenta).

There was also a discussion of viewing in perspective and using color to visualize the 4th dimension.

The movie was followed by an introduction to rotations in special relativity and the definition of a 4 dimensional pyramid as shown in the diagrams:

The pyramid in each dimension is constructed by drawing a pyramid of the previous dimension (blue), adding a point (red) and connecting the new point to each of the old vertices (magenta).

© Philip B. Yasskin, 2005-08.

Last updated July 26, 2008