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).