Not to be picky but loudness is logarithmic with amplitude...
Of course, it also depends on the frequency (different frequencies with the same amplitude aren't percieved as the same loudness), but I figure that simply saying "three times as loud" should serve the purpose of "learning sin waves by asking how would they sound."
also, as far as the "problem can be its own grandma", I realize now that I could have used a much simpler example, such as "what is y, if y = -x", but then I wouldn't have been able to show off my knowlege of hyperbolic functions :)
as a former math tutor myself, I must sympathize with this teacher who may have possibly gone over the deep end after years of trying to teach math. Maybe she's just a flake, of which there are many in the math field - doesn't mean they don't know math or can't teach it though.
a few comments on the author's comments...
1. Forgot how to find the slope of a line.
of course she didn't. she may have said so just to get a little class participation by letting someone in the class explain how.
8. When a student asked, "Can I ask you a question?" she cleverly replied, "You just did!" Needless to say, no one thought that was very funny.
well, I think its funny. depends how she said it.
14. The only reason she was talking about 2 1/2-dimensional objects in the first place was because she thought 1 + 1/2 + 1/2 = 2 1/2.
lots of us math guys make mistakes all the time with simple addition and subtraction. I do all the time. doesn't mean we don't know math.
19. Admitted that she doesn't have enough brain cells to know what pi is.
of course she knows what pi "is", she might not have the value memorized to ten decimal places. maybe that's what she meant.
20. Used her superior math skills to estimate that the answer to one problem was somewhere in between 100 and 1,000.
what was the problem? I could easily come up with a problem that would be almost impossible to estimate even when given that large of a range.
21. Advised us to never ever graph (-3)^x because the result would be way too weird for us to handle.
well, it is. also, I think she knew that by saying this, she's going to create curiosity and actually cause her students to try to graph it, and then try to understand it.
24. Said that math is an escape from the real world and those who do math cannot deal with reality.
wow, there's a lot of truth to that. remember the movie, "A Beautiful Mind"? yeah, sure math is an escape, and a fun one, too.
38. Direct Quote: "The facts of life is this is a parabola." I have no idea what she could have possibly meant by that.
I don't either. why didn't anyone ask her?
44. Told us that although we understood the problem, we'd probably get all confused again once we were further away from her aura.
as a former math tutor, I can attest that this is often true.
I knew that, but didn't want to sound like I was too picky. One correction at a time.
Actually, the change in frequency by a factor of three, is between 1 and 2 octaves, which is higher, but not be a lot.