Introduction

Archimedes' principle is one of the earliest scientific principles, yet it has a surprisingly wide range of applications. This chapter illustrates some of them. The principle is

Not only was Archimedes the greatest mathematician of antiquity, he was something of a one-man Department of Defense. He was related to King Hiero II of Syracuse, a just, prudent, and generous man as well as a patron of the arts. The good ruler often called upon Archimedes for ideas, advice and for solutions to a wide range of problems. Once, Hiero commissioned a wreath-shaped crown of pure gold to be placed on the statue of a god or goddess. He began to suspect that he might have been defrauded—could the goldsmith have replaced some of the gold given to him by an equal weight of silver? The goldsmith knew that the wreath was a sacred object dedicated to the gods, which meant the King could not disturb it in any way. Archimedes' task: without harming the wreath, find out whether the goldsmith had cheated. Initially stumped, the story goes that Archimedes had a flash of inspiration as he felt his own buoyancy in a public bath. He was so excited by his insight that he hopped out, rushing naked into the street and yelling, “Eureka! Eureka!”—Greek for “I have found it! I have found it!”