Later, during the year, there were a in fact couple of occasions here and there when I think I was able to enrich the class with small doses of trigonometry. I made a point of never using sines or cosines, only tangents, because that’s what carpenters deal with in terms of rise over run. For example, there’s a rule of some sort to the effect that the slope of a staircase is supposed to be between 30 and 37 degrees. How do they convert to this from rise over run, which is the way they cut and measure a stringer? I showed them how to do this on their calculators: it’s the Inverse Tangent function. Complex trig? Call it that if you like, but there’s no other way to do it. And it’s not as though I tested them on this material; I just thought they ought to have a chance to see how its done. My favorite trig episode came when they were working in the shop on compound mitre cuts for hip rafters. I think the slope of the roof was something like 5:12, and in the course of the discussion, I asked if anyone could figure out what was the corresponding angle. Just as the students were reaching for their calculators, there came a calm voice from the back of the class: “Twenty six degrees.” A stunned silence fell over the room. The student was Lawson, a nice guy and quite an ordinary student. His hands were at his side and he was looking straight ahead. Having some idea what he must have done, I asked him: “What did you do, pull that number out of your ass?” (That’s the kind of teacher I was.) He smiled and said that he remembered seeing that angle dialed in on the mitre saw down in the shop the previous day when they were cutting their rafters. I especially liked that episode because on any given day, you never knew which student would be the smartest one in the class for at least a brief moment. And I like to think that everyone else might have also learned something.