# SC 2016 Semilab: Math and Discoveries of Archimedes.

Archimedes was arguably the greatest mathematician that ever lived on Earth. After he was killed by Romans, who conquered his native Syracuse, many of his great discoveries were forgotten and it took more than a thousand years and the discovery of modern methods of calculus and mathematical analysis by Newton and Leibnitz for these results to be reproduced. Archimedes’ invention of the Law of Lever and the method of the Center of Gravity laid the foundation for modern mathematical methods of mechanics. His treatment of the equilibrium of floating bodies was fundamental for the development of hydrostatics and its application to shipbuilding; even now introductory chapters of textbooks on naval architecture present diagrams that were first drawn by Archimedes more than two thousand years ago. And while exploring all fundamental advances that he made in the fields of geometry, mechanics, hydrostatics, number theory, and other would definitely take more than a week, in this SemiLab we shall follow the flight of Archimedes’ thought in exploring the volumes of spheres and paraboloids, considering the laws of equilibrium of floating bodies, computing the value of pi, summing the series, and more. We will learn The Mechanical Method, the properties of the Archimedes’ Spiral and the parabolic cuts. Most of these remarkable discoveries can also be explored via hands on activities, which we will also attempt in the course of the Semilab.

**Reference:** [1] Sherman Stein. *Archimedes: What Did He Do Besides Crying Eureka?* Published by: The Mathematical Association of America; 1 edition (June 15, 1999).