Archimedes Research: Explore Math History's Greatest Mind

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smithnya
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Hello everyone,

I'm beginning a research project for a Math History class on Archimedes. Since technically it is a math class, I have to demonstrate and explain some of his math. Naturally, I can't explain and go into detail on everything the man did, and having only about a month to prepare it, I can't read and truly understand everything he worked on or wrote. Could you guys give me some recommendations on interesting topics he covered? Maybe 3 or 4 could get me started.
 
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I recommend the book The Archimedes Codex, especially the chapter that explains how he found the area of a parabola. The book also talks about his concept of infinity.
 
Archimedes is a dual contributor, Geometry/Mathematics and Physics. One of his Geometry exploits was finding the maximum area cone in a sphere. He also gave the first approximation for Pi.