I will take this moment to give you a little background on how I came upon this little trick.
Perhaps this is taught somewhere in some classroom in the world, I don't know. Here is what I do know.
I was in the middle of building a Scrap Wagon you might ask what is a Scrap Wagon? Well it is a wagon that is made 99% from scrap material. My kids were complaining about how heavy all of their baseball equipment is to carry to the park, and yes it is heavy. So I decided to look into buying a wagon for them. After seeing the prices for a wagon I decided that I did not want to spend $70. I am talking Costo or Walmart yard wagon. I could have bought a cheap wagon for $30 but it would just fall apart.. When I buy something I buy something that it is going to last. So, no I didn't buy one.
I came to a point where I needed wheels, while shopping around, even at Harbor Freight, I couldn't find any for what I wanted to pay.
Sticking to the Scrap theme I decided to make the wheels out of wood. Yes wooden wagon wheels, crazy idea huh? Someone was throwing out and old water bed frame. This was perfect for the wheel because they are a 2 inches thick by 9 inches wide by 6 ft. long.
So finally I have the materials for the wheels. I was wanting a perfect circle with an exact center in the pattern. So I ran upstairs and loaded AutoCad 2000 on my PC and find out my SN is expired or some crap. So I D/L a couple free CAD programs, yeah they are crappy and won't put a circle in the very center. Can you believe that? So now I am a little miffed and I have spent way to much time on a CAD circle.
So I stopped and said "How did the Romans and Greeks do it"? They didn't have a CAD program. After sitting and thinking for a while I had an epiphany, Duhh, its so simple.
So one day I am substituting for an Algebra class with some Freshman and Sophomores I challenged them with the same problem. None of them got it, but some came darn close. I gave lots of clues and enjoyed seeing the concentration on their faces. When I explained it to them they each had their own epiphany.
I even gave the problem to a high school calculas class, they showed me everything about an 8 inch circle except how to make it.
So here it is "How to make an 8 inch circle with a 6 inch rectangle."
There is a complete video on the last page.