Hyperbolic Geometry and Daily Life

This story begins with an almost unbearable 10th grade Geometry class — unbearable because of the attitude of the teacher. He shall remain nameless, but if he reads this (unlikely to say the least), I’m hoping he will recognize his part. It was 1963 and I was a good and reasonably devoted student. Our teacher, however, stated often that girls just couldn’t learn math very well, so he walked around the class during exams whispering hints and answers to them. However, the powers of the universe (whatever you believe them to be) provided, as they often do, recompense for this disaster of a learning experience in the form of a Mr. Peter Drees (whose name I shall happily mention). Mr. Drees was, I believe, the math coordinator for the school district, and he got it into his head to discover whether he could teach a group of undistinguished 15-year-olds Hyperbolic Geometry. Mr. Drees was successful at getting a few of us to entertain the concept of a non-Euclidean universe with curved space. He didn’t get many of the details across, but, to my mind he taught something even more important. The geometric version goes like this (with apologies to any…