# Beyond 3-D: Chapter Seven

## Lisa Hicks

I remember reading in my freshman history class that, in the early part of this century, some consultant made lots of money by using a machine to track the movements of factory workers. He used his data to see where the workers were wasting motion and then taught them how to correct it, allowing the workers to work more efficiently. Maybe that machine was a goniometer.

The "Dimensions" dance piece sounds really interesting. Was it ever videotaped?

Even though we have already seen the video of the pendulum graphs, I found the discussion in the book helpful. From the video, I didn't really get a clear idea of exactly what we were seeing.

I didn't know that the radius of a stage light cone was equal to its height. Why don't they teach us useful things like that in high school?

I'm a little confused by the bottom picture on page 144. Which colors are "up," "down," and "in the middle"?

Is there any formula for a line (like the "intercept form" or the "slope-intercept" form) that doesn't miss some of the lines?

I had never though of a "tangent plane" before. Since there are tangent lines, I guess it should have been obvious.

I'm still slightly baffled by the elliptical waves, but it makes a little more sense now. For some odd reason, I feel like I understand the waves "inside" the sphere and the torus better than the waves in the plane. Weird.

Is there any way to visualize (or computer-generate) waves that a sphere would produce in four-space?

I think this chapter will be helpful to the groups in terms of considering dimensionality. I hope so, anyway.

Prof. Banchoff's Response
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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