Here is the GeoGebra visual of the day, accompanied by a math question. You'll notice that it says "Simple" next to the description/header, because I am ultimately interested in a more complex (but definitely related) problem. Eventually, I am interested in exploring how an area of a triangle changes as more than one of its vertices rotate around a circle.
A snapshot (but you should click on the link above to see the animation):
...By the way, in solving this problem, I had to try to figure out how to model a piecewise function in a piece of Geometry software. It looks like GeoGeobra does not have a way of doing this (at least when I searched in the Help index), and Geometer's Sketchpad makes it a helluva pain to get piecewise functions to work. Boooo. In the end, I still couldn't figure out how to get the individual pieces to merge into a single graph in GSP. This is the best that I could do, for now, in GSP. So, if you're a GSP expert and you happen to come across this post, please help!
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PS. I did a lot of math on the flight over to Peru. Can you tell? :) Geoff and I also proved the differential formulas for d(x^n)/dx, like the couple of nerds that we are. It's amazing how much math he remembers, even though it has been years since he has seen any of this stuff! (He is 29 this year, so that is at LEAST 7 years since college, and probably more since he has seen any form of Calculus! He uses a bit of math from time to time, both on his job -- graphics-related programming stuff for his Google-Maps type of mapping interfaces a while back -- and for understanding mortgage, interest rates, etc. in his investment-related leisure reading. But, still! I was surely very impressed.)
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