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Homework Help: Solved 191442

Archimedes, also known as Archimedes of Syracuse was born in Syracuse, Sicily in 287 BC. The exact date of his birth is not known, but the commonly accepted date of 287 BC derives from a statement given by 12th century historian John Tzetzes in that Archimedes had lived for 75 years. Sadly like his exact date of birth, the exact details of the life of Archemides have been lost to history. In one of Archimedes works entitled The Sand Reckoner, he gives his father’s name as Phidias and says he was an astronomer. Other than this one account, nothing more is definitively known about his parents or family history. The Greek historian and biographer Plutarch claimed Archimedes was related to the ruler of Syracuse, King Hiero II, in his work Parallel Lives, though whether this is accurate has never been substantiated. History lost what could have been the greatest chance to know the definitive history of Archimedes when a biography of Archimedes written by one of his friend was lost to history like so much else relating to Archimedes life, leaving historian to have to piece together Archimedes life from what little accounts survived. Simple things like whether Archimedes ever married or had children may never been known. It is believed that Archimedes may have studied in Alexandria, Egypt in his youth, where he would have been contemporaries with the likes of Greek astronomer and mathematicians Conon of Samos and Eratosthenes of Cyrene. This conclusion is reached from Archimedes himself referring to Conon of Samos as his friend, and two of his works having had introductions addressed to Eratosthenes. Archimedes died 212BC when Roman forces captured the city of Syracuse during the Second Punic War. Like nearly everything else about Archimedes life, the exact circumstances of his death are not known for sure. The Greek historian Plutarch presented three different accounts of Archimedess final moments. In one version Archimedes was contemplating a mathematical diagram when the city was captured. Archimedes was commanded by a Roman soldier to come and meet the general of the Roman forces but Archimedes declined, saying that he couldnt leave until he had finished his work. The soldier was so enraged by his refusal that he slew Archimedes with his sword. In another version the Roman soldier had intended to kill Archimedes, and despite Archimedes plea to him to allow him to finish what he was working on so as to not leave his work eternally incomplete, the soldier kills him anyway. In yet a third account by Plutarch, Archimedes was carrying mathematical instruments, and was killed by the Roman soldier because he thought that they were gold. The general of the Roman army was reportedly greatly angered by the news of Archimedes death, as he considered him to have been a valuable scientific asset. Archimedes was laid to rest in a tomb with a sculpture of a sphere and a cylinder of the same height and diameter, an illustration of his mathematical proof that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. Archimedes is most well know for developing a method to determine the volume of an object which does not have a perfectly geometric shape. According to the commonly accepted account, Archimedes was asked to determine whether a crown made for King Hiero II of Syracuse was made of solid gold, or whether it had impurities of silver added into it by a dishonest metal smith. Compounding the issue was the crowns unusual shape, that of a laurel wreath. Archimedes had to find a solution while simultaneously doing minimal damage to the crown itself. In this type of situation, the usual solution would be to melt it down into a fixed geometric shape body whos dimensions were known and in doing so calculate the density of the resulting form. This would not be an option due to the importance and value of the particular item in question. According to that same story, one day while Archimedes took a bath, the fact that the level of the water either rose or fell depending on whether he got in or out of the bathtub caught his eye, and in doing so he realized that he might be able to use his principal to determine the volume of the crown in a non-destructive manner. As water is essentially an incompressible substance, submerging the kings crown would displace an amount of water that would be equal to the volume of the crown itself. The density of the crown can be obtained if the weight of the crown were to be divided by the volume of water it displaces. This was important because the density of the crown would be greater if it were made of pure gold, and considerably less if it turned out it had been mixed with a less dense metal like silver. According to the story, when realized this Archimedes ran into the street crying “Eureka!” or “I have found it!”, completely forgetting that he had been in a bath at the time and therefore in a state of undress. The problem with his commonly accepted historical event is that it never actually appears in any of Archimedes works. One would think that if he made such a brilliant discovery, he would have stopped at some point to write something down about it. Part of the problem that arises from accepting that Archimedes figured out how to deduce the volume of the crown while in the bath is the fact that it would have necessitated and extremely accurate measurement of the the water displacement.

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