In high school geometry, I remember my teacher making some assertion that was plainly false - I think it was that 3 planes always intersect in a line. After arguing with him for like 15 minutes, I walked to the front of the class and wrote a proof on the board. I spent the rest of the class period sitting outside.

If only there was a way to get those teachers reprimanded and retrained.

You're not convinced this actually happened? When I was in elementary school, I regularly (ie. several times per semester) got into arguments with my math and science teachers over stuff this dumb. There's no need to make up something like this when you can find it in the real world so easily.

In grade school I had an argument with my science teacher about wheels. She said that a point along the outside of a wheel moved faster than a point nearer to the center (which is absolutely correct). However, she followed that up by saying that the outside of the wheel makes more revolutions than the inside. I tried to correct her, but she wasn't having any of it. So I grabbed my bike from outside, brought it into the classroom and tied two pieces of string onto one of the spokes on the bike: one near the axel, one near the tire. A few spins of the wheel had her convinced, but I can't believe I actually had to do it.

At least she admitted it- bravo for her (and you!)

If anything, the inside should have to make more revolutions. Since the whole bike is traveling at 10 MPH, at the point with the smaller radius, you'd need more revolutions to travel that same linear speed.

;-)