I thought donuts would be an interesting topic. They are actually the mathematical shape called a torus. I first heard of this sitting in an undergraduate math class. Our professor told us we might try to find out about the torus before the next class. I actually looked it up. I was the only one in the class to do it and was able to talk about it the next time we met. I'm sure I got labeled as a nerd at that point. I wouldn't mind that, but when a room full of mathematicians think you're a nerd, that is probably an especially bad sign.It turns out there is a lot I didn't know about this topic. Like the plural of torus. (It's tori, with a long i sound.) Is it donut or doughnut? (The consensus by those that decide these things seems to be "doughnut" although they seem to put up with "donut". "Donut really didn't come into regular use until Dunkin' Donuts started up in the 1950's.) I thought maybe this had a tie-in to the car, but no. It is spelled "Taurus" and I'm guessing has to do with the zodiac sign.
Imagine two circles linked as a chain. If one makes a full lap following the path of that first circle, we have a torus. Let's say the moving circle is radius r and the stationary circle has radius R.
The surface area is S = 4(pi^2)Rr. (Sorry, I do not know how to make my blog write the pi symbol or how to do exponents.) The derivation of this formula is more easily seen if written S = (2(pi)r)(2(pi)R). It is the circumference of the moving circle taking the a path along the circumference of the big circle.
The volume is V = 2(pi^2)(r^2)R. While this is the simplified version, again it is easier to see where it comes from by writing it differently: V = ((pi)(r^2))(2(pi)r). It is the area of the moving circle again taking the a path along the circumference of the big circle.
What can we use these formulas for? Not important, but there are a lot of them - donuts. Important, but none actually exist - the space station shown in the movie 2001. In the picture notice that it seems more of a rectangle than a circle on the outer edge. I think that is still a torus. The torus definition from different sources I found say "a closed curve", "a closed curve, especially a circle", or simply "a circle".Enough for now. We'll look into this topic more next time.
