This paper is a collection of several interesting solutions to geometric problems discovered and solved by the Greeks. The collection is completely arbitrary. I tried to limit the solutions presented to ones which were intuitive, elegant, or beautiful, but there are some which do not meet these requirements. They serve as reminders of the level to which Greek mathematics rose before the collapse during the dark ages. i myself had no idea of the magnitude of this collapse until I was almost finished with this paper. While doing some last minute research, I discovered a most interesting book it the Tufts library. The binding and back were stamped with intricate patterns far beyond any I had seen before. When I turned it over, the embossed title leapt forth. "Perfected in January-1845," it said on the top of the circle. On the bottom it read," Measure of the circle, by John Davis." What could this great gem be? Could everybody have been wrong, and this tiny book, lost in the stacks held the real answer. Not quite. Upon further examination of the book, published for the author in Providence, Rhode Island, the book is a farce. With many letters of accommodation connected, the book presents slightly complex arithmetic to provide a value of pi being equal to 3.17 for a circumference, and 3.11 for an area! THE EGYPTIANS, 4000 YEARS AGO, WERE CLOSER! And people say we have advanced.

Well, I tried to write this paper with and eye toward a high school level audience which has begun to forget the details of high school math but remembers the general concepts. The problem with writing about math, I have discovered, is that you have to assume a certain level of knowledge on the part of the reader. But how much? Assuming to little results in a huge paper which is far to tedious for those who already know the basics. But, if you assume to much, the only people who will be able to read it will be the ones who already understand it. unfortunately, I think I have failed to be consistent. As a thumb rule, if you can not understand it, it probably is not that interesting.

As another, more obvious side bar, there is an obvious gap in this paper, namely "The Doubling of the Cube." Most of the pictures in this paper were done with a wonderful program called "The Geometer's Sketch Pad," by Nicholas Jackiw, which allows for exact planar constructions. Unfortunately, I lack access to a 3-d program able to complete the task require for a worthy treatment of the problem. Any attempt I made would have been unworthy of the effort I put into the rest of this paper. If I get a chance to complete it in the future, I will try, but don't hold your breath. If you really need to know that bad, check the library for something by Thomas Heath.

Also, while I tried to include as many relevant links as possible, I don't have a direct connection to the internet, and consequently did not have the opportunity to collect all the Urals I needed. I now some biographic links that are absent can be found in the short biography section the Biographies link. There is probably plenty more I haven't found.

Finally, if your reading this for more than personnel enjoyment(that's just about everybody, I imagine) be warned. This is a paper for a college class, and I am only a lousy student. While I do my best, I know I make mistakes. If it is important, check another source to make sure I'm right.

Enjoy.

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