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Archimedes. Presented By: Joel Greathouse, Jim Yang, Daryl Visitacion & Tong Lee Professor Dr. Tuska. Archimedes. Greek Mathematician, astronomer, philosopher, physicist, and engineer. Syracuse (287 BC – 212 BC). Lived in Syracuse his whole life except when he went to a
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Archimedes Presented By: Joel Greathouse, Jim Yang, Daryl Visitacion & Tong Lee Professor Dr. Tuska
Archimedes • Greek Mathematician, astronomer, philosopher, physicist, and engineer. • Syracuse (287 BC – 212 BC) • Lived in Syracuse his whole life except when he went to a school in Alexandria that was founded by Euclid.
Archimedes • King Hiero II and the Gold Crown. • “Give me a lever long enough and a place to stand and I will move the World” (230 BC)
Archimedes • Water displacement in Bathtub… EUREKA…EUREKA!!! Greek for “I discovered it.”
Archimedes • Archimedes Inventions: • The Screw • 2/3 Ratio Of A Sphere And Cylinder • Levers & Pulleys • Weapons Of War • Romans gained control of Syracuse. (212 BC) • “Do not disturb my circles.”
War Weapons >>Animation<< QuickTime Video Link
Writings By Archimedes • On the Equilibrium of Planes (2 volumes) - Law of the lever • On Spirals - Archimedes spiral • On the Sphere and The Cylinder - area and volume of a sphere are in the same relationship to the area and volume of the circumscribed straight cylinder • On Conoids and Spheroids - Archimedes calculates the areas and volumes of sections of cones, spheres and parabolas • On Floating Bodies (2 volumes) - law of equilibrium of fluids
Writings By Archimedes • The Quadrature of the Parabola - Archimedes calculates the area of a segment of a parabola. final answer is obtained by triangulating the area and summing the geometric series with ratio ¼. • Stomachion - Archimedes calculates the areas of the various squares. • Archimedes' Cattle Problem – A letter he wrote who dared his competitors to count the numbers cattle in the Herd of the Sun by solving a number of simultaneous diophantine equations. • The Sand Reckoner - Archimedes counts the number of grains of sand fitting inside the universe. • "The Method"
“The Method” • Also known as the Archimedes Palimpsest. • Gave a sort of behind the scenes on how he did his proofs and what was going on in his mind. • This helped to understand his other books which if other mathematicians had at that time they would had an easier time understanding it. • If book was found at an earlier time the World would be a different place and would have altered the course of modern science.
Calculation Of PI • The first theoretical calculation seems to have been carried out by Archimedes. He obtained the approximation 223/71 < p < 22/7.
Volume Of A Sphere He proved that the area and volume of the sphere are in the same ratio to the area and volume of a circumscribed straight cylinder, a result he was so proud of that he made sure it was engraved on his tombstone. If a sphere is inscribed in a cylinder,then the sphere is 2/3 of the cylinder in both surface area and volume
The Method A copy was put together in the 10th century.
Reused in the 12th century as a prayer book. • Known as the “Palimpsest”, or a text on parchment which has been overwritten with other text.
3. He cut it in half. 1. He took the book apart. 2. He scraped off the Archimedes text. 4. He prepared the parchment of the new book.
5. He wrote the new text. 6. He assembled the new manuscript.. 7. The new manuscript.
12th – 19th century. • Monastery of Mar Saba. • 1800s end up in Constantinople. • 1846 Constantine Tischendorf took one of the leaves. • Cambridge University Library in England. • July 16, 1907, Johan Heiburg made headlines. • Oct 29, 1998, sold for $2 million. • June 20-Sept 5, 1999-Walters Art Gallery in Baltimore.
