Chapter 8 deals with coordinate geometry and its various uses when applied to the fourth dimension.  This is the chapter that is probably the most helpful for the purposes of the "Geometry Updated" project group.  Much of what is discussed in the chapter is valuable information when applying principles of basic coordinate geometry to the fourth dimension.

First, there is the basic, yet not so obvious, relation of the Pythagorean thereom to third dimension.  The results in the book giving 2 as the distance for the longest diagonal of a hypercube at first surprised me and then, after a little more thought, I realized tha this wasn't such a surprising answer when you consider the complexity of the hypercube.

Another area of the chapter that was of great interest was that of the quaternions.  The whole concept of a number system that could exist within the framework of four-dimensions seems complex in itself, but it seems even more so when we are shown the results of the various formulas taken from vector calculus.  The use of quaternions for rotational computer graphics seems to be quite a large field and one that in the upcoming years will be utilized even more and more.