What do you think of when you hear the name Archimedes ? A ship floating on the sea ? Great war machines protecting ancient Syracuse ? Water screws irrigating the desert ? Burning mirrors setting fire to Roman warships? Spheres, cylinders, circles, spheroids, conoids, spirals ? Perhaps a field of cattle or a universe full of sand ? These were all things that Archimedes considered during his life. 

Archimedes was an ancient Greek mathematician and inventor born in Syracuse on the island of Sicily. His birth date is estimated to be 287 B.C. by the fact that John Tzetzes, a twelfth-century Byzantine historian, stated that he died at the age of 75 during the sack of Syracuse in 212 B. C. ¹ Archimedes was the son of Pheidias, an astronomer known for his investigations into the sizes and distances of the sun and the moon. It was also said by Plutarch that Archimedes was related to Hieron, King of Syracuse.

It is known that Archimedes spent some of his life in Alexandria, the center of scientific activity during his era. It was in Alexandria that Ptolemy I Soter (died 283 B.C.) invited a circle of philosophers and literary men from Greece to study. He founded the "Museum" and "Library" an academy where arts and sciences were cultivated. Scholars from Greece, Babylonia, and Rome gathered to study under the professors of the "Museum" 

Among the sciences cultivated in Alexandria were geometry, algebra, trigonometry, astronomy, astrology, geography, surveying, mechanics, and alchemy. The Alexandrians were generally specialists straying away from the old Greek philosophy that "all learning" is province ².

One of the first of the famous Alexandrian scholars was Euclid with his Elements of Geometry and it is suspected that while Archimedes was in Alexandria he studied with the pupils of Euclid. It is also assumed that while in Alexandria Archimedes became friends with the Conon of Samos and with Eratosthenes. It was to Conon that he sent his discoveries before publication, and after the death of Conon to Dositheus of Pelusium, the friend and pupil of Conon. Through Eratosthenes Archimedes introduced the Cattle Problem to the mathematicians of Alexandria, and it was for Eratosthenes that Archimedes wrote the Method ³.

Upon his return to Syracuse from Egypt, Archimedes devoted his life to the study of mathematics. He felt that his mechanical inventions, which were in fact what provided him with his fame, were “merely the diversions of a geometer at play". In Plutarch's words, "he possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge that , though these inventions had obtained for him the renown of more than human sagacity, he yet would not deign to leave behind him any written work on such subjects, but regarding as ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit." ⁴  Because of this belief, Archimedes wrote only on strictly mathematical subjects, with the exception of one work, On Sphere Making. It is the assertion of Pappus that this work is a description of the construction of a devise composed of concentric glass spheres, moved by water power, representing the apparent motions of the planets, moon, sun, and perhaps the constellations. It was said by Cicero that Marcellus took as booty from the sack of Syracuse an instrument of this type. ⁵

It seems that it was the devotion to Hieron that induced Archimedes to divert his mathematical studies to his engineering skills. There are many "stories" of Archimedes' achievements in this field that are difficult to substantiate but many indicate that the inventions were created at Hieron's request. A well published story by Vitruvius is that of Hieron's desire to know if all the gold he had given to a goldsmith to create a crown was actually used instead of being substituted with an amount of silver. 

The story says that the problem was presented to Archimedes causing considerable puzzlement. While pondering the problem he visited a public bath and noticed that the water in the tub rose in proportion to the amount that he immersed his body into it. This indicated a solution to the problem because Archimedes observed that by noting the difference in overflow when the crown and equal weights of gold or silver were immersed he would be able to distinguish if the crown were of pure gold.
  

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