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Politics : Evolution -- Ignore unavailable to you. Want to Upgrade?

To: Brumar89 who wrote (27107)	6/13/2012 2:01:33 PM
From: Solon	1 Recommendation Read Replies (1) \| Respond to of 69300

"Drown those who speak of irrational numbers" Get an education...PLEASE! The Pythagoras allegation is an "evolved TALE"! " Pappus merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning. [10] Iamblichus gives a series of inconsistent reports. In one story he explains how a Pythagorean was merely expelled for divulging the nature of the irrational; but he then cites the legend of the Pythagorean who drowned at sea for making known the construction of the regular dodecahedron in the sphere. [11] In another account he tells how it was Hippasus who drowned at sea for betraying the construction of the dodecahedron and taking credit for this construction himself; [12] but in another story this same punishment is meted out to the Pythagorean who divulged knowledge of the irrational. [13] Iamblichus clearly states that the drowning at sea was a punishment from the gods for impious behaviour. [11] These stories are usually taken together to ascribe the discovery of irrationals to Hippasus, but whether he did or not is uncertain. [14] In principle, the stories can be combined, since it is possible to discover irrational numbers when constructing dodecahedrons. Irrationality, by infinite reciprocal subtraction, can be easily seen in the Golden ratio of the regular pentagon. [15] Some modern scholars prefer to credit Hippasus with the discovery of the irrationality of v2. Plato in his Theaetetus, [16] describes how Theodorus of Cyrene (c. 400 BC) proved the irrationality of v3, v5, etc. up to v17, which implies that an earlier mathematician had already proved the irrationality of v2. [17] A simple proof of the irrationality of v2 is indicated by Aristotle, and it is set out in the proposition interpolated at the end of Euclid's Book X, [18] which suggests that the proof was certainly ancient. [19] The proof is one of reductio ad absurdum, and the method is to show that, if the diagonal of a square is commensurable with the side, then the same number must be both odd and even." [19] LOL!! "In the hands of modern writers this combination of vague ancient reports and modern guesswork has sometimes evolved into a much more emphatic and colourful tale. Some writers have Hippasus making his discovery while on board a ship, as a result of which his Pythagorean shipmates toss him overboard; [20] while one writer even has Pythagoras himself "to his eternal shame" sentencing Hippasus to death by drowning, for showing "that v2 is an irrational number." [21]