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  “Give me a lever long enough and a place to stand and I will move the World” (230 BC)  King Hiero II and the Gold Crown.

Archimedes  Water displacement in Bathtub… EUREKA…EUREKA!!! Greek for “I discovered it.”

Archimedes  Romans gained control of Syracuse. (212 BC) The Screw 2/3 Ratio Of A Sphere And Cylinder Levers & Pulleys Weapons Of War  Archimedes Inventions:  “ Do not disturb my circles.”

War Machines & Inventions

War Weapons

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Mirrors

Archimedes Screw

Writings By Archimedes On the Equilibrium of Planes (2 volumes) - Law of the lever On the Equilibrium of Planes (2 volumes) - Law of the lever On Spirals - Archimedes spiral 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 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 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 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. 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. 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. 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 Sand Reckoner - Archimedes counts the number of grains of sand fitting inside the universe. "The Method" "The Method"

“The Method” Also known as the Archimedes Palimpsest. Also known as the Archimedes Palimpsest.Archimedes PalimpsestArchimedes Palimpsest Gave a sort of behind the scenes on how he did his proofs and what was going on in his mind. 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. 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. 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. 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 10 th century. A copy was put together in the 10 th century.

Reused in the 12 th century as a prayer book. Reused in the 12 th century as a prayer book. Known as the “Palimpsest”, or a text on parchment which has been overwritten with other text. Known as the “Palimpsest”, or a text on parchment which has been overwritten with other text.

1. He took the book apart. 3. He cut it in half. 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.

12 th – 19 th century. 12 th – 19 th century. Monastery of Mar Saba. Monastery of Mar Saba. 1800s end up in Constantinople. 1800s end up in Constantinople Constantine Tischendorf took one of the leaves Constantine Tischendorf took one of the leaves. Cambridge University Library in England. Cambridge University Library in England. July 16, 1907, Johan Heiburg made headlines. July 16, 1907, Johan Heiburg made headlines. Oct 29, 1998, sold for $2 million. Oct 29, 1998, sold for $2 million. June 20-Sept 5, 1999-Walters Art Gallery in Baltimore. June 20-Sept 5, 1999-Walters Art Gallery in Baltimore.