2. (This is a bit of a research question.) A polar planimeter is a pretty cool mechanical device that can be used to measure the area of an arbitrary region in the plane enclosed within a closed curve. It is (was) used in medicine, biology, agriculture, engineering, etc. What is particularly cool about it is that it uses Green's theorem behind the scenes to calculate the area of the region! So the question is: use Green's theorem to explain how a polar planimeter works. To answer this question you will need to figure out first what a polar planimeter is. A quick google search of something like "polar planimeter Green's theorem" will lead you to many references that explain this in detail. Read one, or more than one, figure out how it works, and explain it to me! You could even try to build your own planimeter if you want, it's a pretty neat instrument! (and if you do, please send me a picture or a video! :-)