{"id":365,"date":"2014-11-30T12:00:19","date_gmt":"2014-11-30T20:00:19","guid":{"rendered":"http:\/\/mostlymental.com\/?p=365"},"modified":"2014-11-30T16:23:49","modified_gmt":"2014-12-01T00:23:49","slug":"archimedes","status":"publish","type":"post","link":"http:\/\/mostlymental.com\/?p=365","title":{"rendered":"Archimedes"},"content":{"rendered":"

Hello everyone!<\/p>\n

Mathematics is often presented as if it's a body of knowledge which people have known forever.\u00a0 But that's not the case; modern math has come about through the work of millions of clever people over thousands of years.\u00a0 I don't have time to talk about everyone, of course, but I thought it would be interesting to at least discuss a few of the great mathematicians.\u00a0 There aren't many mathematicians greater than Archimedes, so he seems a natural first choice.\"\"<\/p>\n

(Portrait by Domenico Fetti (1620).\u00a0 Image taken from Wikipedia.)<\/p>\n

Archimedes\u00a0of Syracuse (c. 287 - 212 BC) is perhaps most famous for a case of public nudity.\u00a0 As the story goes, a king suspected his crown was not pure gold, but had instead been made with a mixture of gold and silver.\u00a0 He asked Archimedes to find a way to check without damaging the crown.\u00a0 When Archimedes stepped into the bath that evening, he noticed that the water level rose in response.\u00a0 He realized that he could submerge the crown in water and use the change in water level to find its volume, and thus its density, which would tell him what the crown was made of.\u00a0 Not bothering to get dressed, he ran through the streets shouting, \"Eureka!\" (\"I have found it\").
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While this story is likely untrue, Archimedes did study the physics of water, particularly relating to the buoyancy of ships.\u00a0 In fact, most of the work he did in physics and engineering was extremely practical.\u00a0 For instance, he designed numerous weapons, such as powerful catapults and a giant claw to defend Syracuse from invasion.\u00a0 He also invented an odometer (to measure the lengths of long paths) and several other useful devices.<\/p>\n

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Like most of the ancient Greeks, his mathematical work was primarily geometric.\u00a0 His favorite method was to use the law of levers: if two weights sit on a balanced lever, the weight of each times the distance from the fulcrum is equal.\"lever\"<\/a>He used this law to find ratios of geometric objects.\u00a0 For instance, he was able to show that for a sphere inscribed in a cylinder, as shown below, both the volume and the surface area were in the ratio \"\"<\/span>