I'm telling you this story not just for your entertainment but to show you that you shouldn't be afraid to embarass yourself ... your teacher has been much more thorough at this than you ever will be.
We get a fair number of calls from the public on mathematical issues. Years ago I passed by the office and the secretary asked if I could answer such a question. I said sure, and we had this conversation:
Caller: Yes, Hi, this is Joe of Radio XYZ. We are on the air and we have this math contest, and there's a question we can't answer. Can you help us?
Me: I'll try.
Joe: There's this ladder, and it's 5 feet long, and it's leaning against the wall and it's bottom is 3 feet away from the wall. At what height does it touch the wall?
Me: Oh, that's easy, you just use the Pythagorean Theorem.
Joe: That's what we thought, but just how does it work?
Me: Well, you square 5, that's 25, and you square 3, that's 9, 25+9=34, and you take the square root. I don't know the square root of 34, but it's just under 6.
Joe: So the ladder touches the wall at a heigh of about 6 feet?
Joe: That's awfully high!
Me: Yes, but it's just the Pythagorean Theorem.
Joe: What's your name?
Me: Peter Alfeld.
Joe: Pete! Pete, can we quote you? Can we say that Pete of the University of Utah Math Department says the ladder touches the wall at a height of 6 feet?
So I hang up and realize that I just invented a five foot ladder that can reach a height of six feet. The savings in aluminum alone ... But I don't remember the name of the station, so I can't call back. Presumably my folly was broadcast over the entire Salt Lake Valley! I avoided the streets of Salt Lake City for a few months, and to this day I make sure to mention in every course I teach that the greatest obstacle to progress in mathematics is the human inability to distinguish reliably between a plus and a minus sign. You may have heard me pronounce that in your class!
Fine print, your comments, more links, Peter Alfeld, PA1UM