A Presentation By: Charlotte Lenz http://www.math.nyu.edu/~crorres/archimedes/pictures/ ArchimedesPictures.html
Born: 287 BC to an Astronomer named Phidias Grew up in Syracuse, Sicily Only left Sicily as a teenager to go to Alexandria, Egypt to study under the followers of Euclid http://www.italiancookingandliving.com/imm/map_sicily.jpg
Returned to Syracuse after his studies in Alexandria for the remainder of his life Died: 212 BC, was killed by a Roman soldier during the Second Punic War when he refused to stop working on a mathematical diagram to go speak to General Marcus Remained dedicated to his work up the moment he died
Archimedes Screw Originally used to pump water out of ships. Also used in Irrigation Still used today. http://www.school for champions.com/biographies/images/archimedes1.gif
Lever and Pulleys Although Archimedes did not invent lever and pulleys, he did provide an explanation that facilitated their use. Said, Give me a place to stand, and I will move the Earth. His knowledge of lever and pulleys led Archimedes to believe that he could move anything given the right resources and his knowledge of how lever and pulleys worked.
Used geometric ideas to prove or discover other mathematical information. Wanted to find the area of sections bounded by geometric figures, such as parabolas and ellipses. Did this by breaking the sections into an infinite number of rectangles and [adding] the areas of these rectangles together. This method of calculating area is known as Integration. http://www.vias.org/calculus/img/04_integration 10.gif
His method of integration allowed him to find areas, volumes, and surface areas of many bodies. Used the Method of Exhaustion to approximate the areas of circles by comparing them to inscribed and circumscribed polygons. This led to the realization that the ratio of a circle to the square of its radius always gives a value that is estimated as π http://personal.bgsu.edu/~carother/pi/pigifs/inc circ 8gonx.gif
Approximated π by inscribing and circumscribing polygons of various sizes in and around a circle Determined the perimeters of these polygons and used them as upper and lower bounds to the length of the circumference Started with smaller polygons and worked up to bigger polygons Used polygons of sizes (meaning # of sides) 12, 24, 48, and 96
After making his calculations using a polygon with 96 sides, Archimedes was able to approximate π using the inequality 310 71 <π<31 7 To this day π is still an approximated value
http://thumbs.dreamstime.com/thumb_195/1192388679l854qe.jpg King Hiero II of Syracuse gave gold to craftsmen for them to make a crown He thought they stole some of the gold and substituted silver into the making of the crown Asked Archimedes to find a way to prove the crown was not pure gold without melting it down
Archimedes went to get into a full bathtub one day and noticed that the amount of water displaced was related to the amount of his body that was put into it He shouted Eureka! and ran through the streets of Syracuse naked Took a lump of gold equal to the amount of gold Hiero originally gave the craftsmen and found the amount of water it displaced Took the crown (which was supposed to be made of the same amount of gold) and found that it did not displace the same amount of water The King had been duped, but the craftsmen were never heard from again http://www.math.nyu.edu/~crorres/archimedes/crown/archbathnbc3.jpg
Archimedes Principle says: an object is immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. http://physics.nku.edu/generallab/211%20archimedes%20principle2.gif
On Plane Equilibrium Quadrature of the Parabola On the Sphere and Cylinder On Spirals On Conoids and Spheroids On Floating Bodies Measurement of a Circle The Sandreckoner On the Method of Mechanical Problems
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