Explanations the Tesseract (Hypercube)

The purpose of this page is to provide a wide variety of links, downloads, pictures, and descriptions that will help provide a glimpse of the nature of the tesseract and of four dimensional non-Euclidean geometry.

The four-dimensional cube, or tesseract, although by no means a simple concept, can be explained using simple (layman's) terms. What these simplified explanations lack in mathmatical expertise they make up for in easily understandable description.

For a simple description of a tesseract and a guided demonstration (with the right software), click here.

By its very nature, a four dimensional hypercube, or tesseract, cannot be viewed in its entirety in three dimensional space any more than a three dimensional cube can be seen in its entirety in two dimensional space. In both cases, they can be represented, but not created. To view an explanation and illustration of what a hypercube would look like if passing through three dimensional space, click here.

The concept of a tesseract is also brilliantly described by children's author Madeleine L'Engle in her Newbery Award-winning book, A Wrinkle In Time. She uses the concept of four-dimensional tesseracts as a means of travel through time and space in the three-dimensional world. This process, called tessering, is innocently and subtly slipped into the format of a book written for children. Despite the audience for which the story was intended, this explanation is very useful to explain a tesseract. To see the chapter (aptly titled "The Tesseract"), click here.

The most useful means for visualizing a tesseract is by far to see a model. Click here to go to a web site that contains a BASIC program for drawing tesseracts and other n-dimensional cubes.

The BASIC program mentioned above, however helpful, is not without its limitations. It is useful for showing a hypercube frozen in space, but does not show any of the rotations of the hypercube. One program that can do this is Tony Robbin's Fourfield: Computers, Art and the Fourth Dimension. Download the IBM-compatible programs hyper and hypers, and their instructions. (Note: The effectiveness of this program is greatly enhanced by the use of 3-D glasses.)

So, you think you understand the concept of a tesseract? To test your understanding with a purely mathematical definition of a tesseract, click here. (WARNING: This site also contains information about many other types of geometric figures. The explanation of the hypercube is the third explanation.)

This page was constructed by James R. Coltharp, Jr., who is an undergraduate student at the University of Kentucky.

Comments? Suggestions? Send e-mail to jrcolt00@ukcc.uky.edu.