Who is Archimedes?
Archimedes
(287 - 212 B.C.)

"Give me a place to stand and I will move the earth" - a quote by Archimedes

http://www.sciencetrek.net/archimedes.htm

• Archimedes was a greek mathematician, physicist, and engineer who live between 287-212BC.
• Perhaps the greatest scientist of Antiquity.
• One of first to accurately calculate volumes of geometric shapes (spheres, cylinders, etc.)
• First to accurately calculate ratio of circumference to diameter of a circle.
• Known for his discovery of the Boyant Force in nature.
• Also a prominent inventor in his time:
• One of his practical inventions is still in use today: Archimedes Screw (see pic below)- an inclined rotating coiled tube originally used to lift water from holds of ships.
• Invented the Catapult
• devised systems of levers, pulleys, and weights for raising heavy loads.

http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html
MATHEMATICS AND ARCHIMEDES:
The "Method of Exhaustion"-Integration
Archimedes was able to approximate the areas of circles by summing the areas of inscribed and circumscribed rectangles.  By taking rectangles that get smaller and smaller and summing the areas he was able to find both areas and volumes of many difference shapes.  Nearly 2000 years later Newton and Leibniz would use integration in calculus to do this.
Archimedes was able to approximate the value of between 3-1/2 and 3-10/71, the most accurate of his time.  He also devised new ways of approximating square roots.

The Gold Crown:

http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html
Around the first century BC it is said that archimedes uncovered a fraud in the manufacturing of a gold crown for King Hiero II of Syracuse.  It is believed that Hiero would have placed the wreath on a statue of a god or goddess and he believed the goldsmith had replaced some of the gold given to him by an equal weight of silver.  So Heiro went to Archimedes and asked him to determine if the wreath was pure gold. The story is told that as he lowered himself in to a bath he noticed water was displaced by his body and it flowed over the edge of the tub.  This was the inight Archimedes needed to see that the crown should not only weigh its worth in gold but also displace the same volume as equal weight of gold would.  They say he was so exited he ran through the streets naked screeming "Eureka" which means "I've found it."

Archimedes, who combined a genius for mathematics with a physical insight, must rank with Newton, who lived nearly two thousand years later, as one of the founders of mathematical physics.