We are now introduced to perhaps the greatest mathematician of antiquity, Archimedes. There are many things for which he is famous, but for our Great Theorem, Dunham has chosen his proof that the area formula for circles is . Of course, Archimedes won’t write the formula quite this way, and we will see what he does to get around the notation. As we look at the Great Theorem of this chapter, one question many people have when they look at Archimedes’ work is how he came to his conclusions. In particular, Archimedes spent a lot of time estimating values that today we would usually find using a calculator. There are a number of different ways to estimate things like and square roots. In the second reading, we consider some ways that Archimedes might have arrived at his conclusions. For the second reading, you should read at least the introduction and Section 4.
Readings
First reading: Dunham, Chapter 4, pages 84 - 99
Second reading: Archimedes’ calculations of square roots