# Beyond 3-D: Chapter Eight

## Lisa Hicks

If I were to sum up my response to Chapter Eight in one word, that word would probably be, "Hunh?" I got a little lost there towards the end. I think my brain is only programmed to deal with a maximum of two variables at a time. However, once again, I did learn some really interesting things that I feel like I should have been taught already. For example, I had never thought of a point as a sum of two other points. For a point like (3, 4), I was just told, "Go over three and up four." This is essentially the same as, "Think of this point as the sum of (3, 0) and (0, 4)," I suppose, but I think the second method makes a little more sense. It has a little more "why" involved.

I really like the fact that you can simplify things by moving them up a dimension. By moving a two-simplex into three-space, you lose those nasty fractions and irrationals. This is great! It is also a bit surprising, though, because people usually think of adding dimensions as a way to complicate things.

I started getting lost on page 167 with the C(n, k) equation. That is an equation, right? I'm confused on what all of the variables stand for and how they relate to one another. The C reminds me of compounding interest or something else suspiciously like calculus, but I doubt that this is right.

I did a group project on the "golden ratio" in high school, and I still don't really know what it is. I know that you can find it all over the place in Greek and Roman art and architecture, and that a really famous composer (whose name totally escapes me) used it in his work. We got an A on the project, proving that, in high school, you don't really have to know what's going on.

I don't understand the graphs on 174-5.

I'm amused by the idea that mathematicians "invent" things like sine and cosine and types of geometry. Some people tend to think that all of these mathematical things are "discovered," like electricity.

The section on "Coordinates for Circles and Spheres" was very baffling to me. Then again, most things involving sines and cosines are very baffling to me.

I thought that this chapter was both puzzling and enlightening. Hopefully, the final chapter will continue the enlightening.

Ignore the rest of this. I'm just writing it to confuse the machine in hopes that all of the important part will miraculously get transferred to the Web page.

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