# Transformation Geometry

Unexpectedly Earning an Epithet in a Math Course

Ahh, those halcyon days of higher education...

One of my most memorable courses was a math course titled Transformation Geometry. It was concerned with the geometry of transformations, particularly those that preserved the distances between two points. We studied translations, rotations, and reflections, their groups, and the seventeen 2D crystal patterns. As mathematics courses go, it wasn't hard, and it had great visual appeal (unlike, say, Foundations of Analysis).

The subject's apparent simplicity almost did me in. On the first of three major tests I did well, and became complacent. Mistake! My results on the second test were appalling. I became quite worried.

When we got to the last test, I was doing better, but still hadn't mastered the material completely. My score on the third test was again good, but not spectacular. It looked like I would have to take the final.

At the end of the semester, the professor put up a short list of grades on the board. If your score was better than the highest, you didn't need to take the final and you'd get an A. Below that, taking the final was optional, but probably to your advantage. My average was close to the no-final cut point, but I wanted an A. I needed to take the final. So I hunkered down and really started studying.

After a few days of study, something amazing happened. I got it. I really got it. I understood the material forwards and backwards. Give me a problem, I'll give you a solution. 100% confidence. I grokked it.

I sailed into the room of the final and sat down. There were about six questions, of which we had to answer five. At the starting time I looked at the first problem.

Hmmm, I thought, I'm not quite sure how to do this... maybe I'll have a clearer idea for the next one.

Nope, not really. Maybe the next?

I don't get this one, either.

I'll come back to this one.

Uh-oh.

Okay, I think I can handle this one.

I worked on the sixth problem and came up with a solution. Then I went back to the earlier problems and started work. By the end of the test period, I had solutions for five. I wasn't really confident of my answers, but at least I'd answered five questions.