Archimedes Syracuse (then part of Greece) 287-212 BC

Quick facts about Archimedes . . . Born About 287 BC in Syracuse, Sicily. At the time Syracuse was an independent Greek city-state with a 500-year history

Quick facts about Archimedes . . . Born About 287 BC in Syracuse, Sicily. At the time Syracuse was an independent Greek city-state with a 500-year history Died 212 or 211 BC in Syracuse when it was being sacked by a Roman army. He was killed by a Roman soldier who did not know who he was.

Quick facts about Archimedes . . . Born About 287 BC in Syracuse, Sicily. At the time Syracuse was an independent Greek city-state with a 500-year history Died 212 or 211 BC in Syracuse when it was being sacked by a Roman army. He was killed by a Roman soldier who did not know who he was. Education: Probably studied in Alexandria, Egypt, under the followers of Euclid.

Quick facts about Archimedes . . . Born About 287 BC in Syracuse, Sicily. At the time Syracuse was an independent Greek city-state with a 500-year history Died 212 or 211 BC in Syracuse when it was being sacked by a Roman army. He was killed by a Roman soldier who did not know who he was. Education: Probably studied in Alexandria, Egypt, under the followers of Euclid. Family His father was an astronomer named Phidias and he was probably related to Hieron II, the king of Syracuse. It is not known whether he was married or had any children.

Inventions Many war machines used in the defense of Syracuse, compound pulley systems, planetarium, water screw (possibly), water organ (possibly), burning mirrors (very unlikely). Fields of Science InitiatedHydrostatics, static mechanics, pycnometry (the measurement of the volume or density of an object). He is called the “father of integral calculus” and also the “father of mathematical physics”. Major Writings. On plane equilibriums, 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. Place in History. Generally regarded as the greatest mathematician and scientist of antiquity and one of the three greatest mathematicians of all time (together with Isaac Newton (English 1643-1727) and Carl Friedrich Gauss (German 1777-1855)).

This statue in the National Museum in Naples, Italy, was widely claimed to be Archimedes. It is actually a bust of Archidamos III, a third century BC king of Sparta Italian postage stamp honoring Archimedes May 2, 1983 Scott Catalogue Number 1559 Archimedes is commemorated on a Greek postage stamp from 1983. The Fields Medal carries a portrait of Archimedes.

https://en.wikipedia.org/wiki/Punic_Wars In the 300 BC, Roma and Carthage were considerably expanding their territory … which of course lead to conflicts. Roma and Carthage fought three wars (the Punic war). Roma won all three and established its absolute dominance over the Mediterraneum https://en.wikipedia.org/wiki/Punic_Wars

Territories under the control or Roma (in red) and Carthage (in blue) before the second Punic war

The second Punic war The Romans locked horns with Carthage in the First Punic War (264-241 BC), during which they greatly expanded their territory, although they did not capture the city of Carthage itself. The Greek city of Syracuse, where Archimedes lived, initially supported Carthage. But early in the war Rome forced a treaty of alliance from Syracuse's king, Hiero II, that called for Syracuse to pay tribute and provide grain to the Romans.

The Romans and Carthaginians renewed their antagonisms in 218 BC, the beginning of the Second Punic War. Under Hannibal, Carthage gained the first round of victories, culminating in Hannibal's crossing of the Alps into Italy (218 BC) and his defeat of the Romans at Cannae (216 BC). Hannibal's successes in Italy helped convince many Syracusans that they were allied with the wrong side. …

Hiero honored his treaty with Rome while he lived Hiero honored his treaty with Rome while he lived. However, upon his death in 215 BC he was succeeded by his 15-year-old grandson Hieronymos who began negotiations with Hannibal.

Hiero honored his treaty with Rome while he lived Hiero honored his treaty with Rome while he lived. However, upon his death in 215 BC he was succeeded by his 15-year-old grandson Hieronymos who began negotiations with Hannibal. This alarmed the pro-Roman faction within Syracuse, and so in 214 BC while Hieronymos was visiting the neighboring Greek city of Leontini they had him assassinated, ending his 13-month reign.

Hiero honored his treaty with Rome while he lived Hiero honored his treaty with Rome while he lived. However, upon his death in 215 BC he was succeeded by his 15-year-old grandson Hieronymos who began negotiations with Hannibal. This alarmed the pro-Roman faction within Syracuse, and so in 214 BC while Hieronymos was visiting the neighboring Greek city of Leontini they had him assassinated, ending his 13-month reign. His assassination led to civil war in Syracuse between the pro-Carthaginian and pro-Roman factions, during which most of Hiero's family was killed. The pro-Carthaginian faction was eventually victorious and two brothers of mixed Carthaginian-Syracusan descent, Hippokrates and Epikydes, took control of the city.

The Romans sent Marcus Claudius Marcellus to deal with the Syracusan situation. He first took Leontini by force and had some 2000 Carthaginian sympathizers beheaded. Marcellus then besieged Syracuse in 213 BC. He attacked the coastal walls of Syracuse with sixty battleships while his co-commander attacked the inland walls with ground troops.

(Archimedes the geometer). Archimedes had been King Hiero's military adviser for many years and had well prepared Syracuse for any attack. A 1740 engraving of Archimedes planning the defenses of Syracuse. The Greek writing on his cap is (Archimedes the geometer).

war gadgets may have worked. Archimedes designed many tools for defending Syracuse from invasion. This is a model of how one of Archimedes war gadgets may have worked.

A detail of a wall painting in the Stanzino delle Matematiche in the Galleria degli Uffizi in Florence, Italy. Painted by Giulio Parigi (1571-1635) in the years 1599-1600.

It is rumored that Archimedes used mirrors to reflect and intensify the sun, causing the ships to catch on fire, but it’s unlikely that at the time the technology allowed to build large enough mirrors

Wall painting from the Stanzino delle Matematiche in the Galleria degli Uffizi (Florence, Italy). Painted by Giulio Parigi (1571-1635) in the years 1599-1600.

Engraving from Mechanics Magazine London, 1824 Give me a place to stand and I will move the earth Engraving from Mechanics Magazine London, 1824

w1 x d1 = w2 x d2 The Law of the Lever w2 w1 d1 d2 fulcrum The lever is in equilibrium if w1 x d1 = w2 x d2

w1 x d1 = w2 x d2 w1 x 5 = 400 x 5 w1 = 400 w1 x d1 = w2 x d2 400 pounds 5 feet ? w1 x d1 = w2 x d2 w1 x 5 = 400 x 5 w1 = 400 2 feet 8 feet ? 400 pounds w1 x d1 = w2 x d2 w1 x 8 = 400 x 2 w1 = 100

Lever Problems Now it is your turn How long would the lever need to be so that you can lift a 20 ton dinosaur? Place the dinosaur 10 feet from the fulcrum and pretend you weigh 100 pounds. How long would the lever need to be so that you can lift a team of 10 football players (weighing 200 pounds each)? Use the same set-up as above. How long would the lever need to be so that you can lift a lifetime supply of candy bars? Estimate that you can eat 2 pounds of candy each week for 70 years. Use the same set-up as above.

Archimedes’ surviving work http://physics.weber.edu/carroll/archimedes/treatises.htm

The story of the golden crown Archimedes figured out how to determine if a crown was all solid gold.

The story of the golden crown does not appear in the known works of Archimedes. Moreover, the practicality of the method it describes has been called into question, due to the extreme accuracy with which one would have to measure the water displacement. Archimedes may have instead sought a solution that applied the principle known in hydrostatics as Archimedes' principle, which he describes in his treatise On Floating Bodies. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.

The magnitude of the buoyancy force is proportional to the difference in the pressure between the top and the bottom of the column, and (as explained by Archimedes' principle) is also equivalent to the weight of the fluid that would otherwise occupy the column, i.e. the displacedfluid. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink. If the object is either less dense than the liquid or is shaped appropriately (as in a boat), the force can keep the object afloat.

Using this principle, it would have been possible to compare the density of the golden crown to that of solid gold by balancing the crown on a scale with a gold reference sample, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."

Archimedes proved formulas for the volume of cylinders, cones and spheres

The “Method Concerning Mechanical Theorems” In this work Archimedes tried to calculate volumes of ellipsoids as a sum of volumes of infinitesimal slices. The only surviving copy of the manuscript has only been found and translated in recent years. The story of the book and how it was found is quite fascinating. See the video: Archimedes infinite secret

The death of Archimedes depicted on a Roman floor mosaic

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