# 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.