## Response from Prof. B.

Several times I have seen versions of the illusion you describe, I believe. In some cases it is as simple as taking a dollar bill and creasing it near the end so that part of it is in shadow. As you look at it, you can convince yourself that what you are seeing is a different view, where the concavity and convexity are reversed. Then if you move the bill slightly, it seems to rotate in a very strange way. The strong illusion is maintained for quite a while.

I'm definitely interested in seeing what comes next in the rotation project. You might want to see what happens for a rotation of an object in 3-space about an arbitrary axis, although the images of most interest will almost certainly be those that possess some degree of symmetry with respect to the axis. When you are working with objects in 4-space, you will want to look at rotations about a plane rather than about a line. The same sorts of matrices will give you the basic building blocks, keeping two coordinates fixed and taking combinations of the other two with cosines and sines. If you have trouble with the linear algebra, check with me.

Good links to other student papers--I like the interconnectivity.