Billard - théorie et jeu by Régis petit, Michel Lambert PDF

By Régis petit, Michel Lambert

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In any case, the passage does not describe a rule for all right triangles; it refers only to the 3, 4, 5, triangle. The earliest extant account of Pythagoras and the ox is from around 45 BCE. The Roman statesman Cicero wrote: “Nor did anyone ever pledge a tithe to Hercules, if to become a sage—although Pythagoras, upon finding something new in geometry, is said to have immolated an ox for the Muses; but I do not believe it, since he did not even want to immolate an animal for Apollo at Delos, to not sprinkle the altar with blood.

Actually, we don’t even know whether Hippasus discovered any such thing! ”20 But that was just not true at all. Von Fritz gave no example of anyone who attributed the discovery to Hippasus. Therefore, one historian objected that von Fritz’s claim “seems to me to be devoid of all foundation. So far from being unanimous, the tradition is, I believe, non-existent. ”21 What is the source of the now popular story about Hippasus, voiced by Kline, Von Fritz, and so many others? One earlier account appears in the work of John Burnet, in a book titled Early Greek Philosophy.

A story about Hippasus becomes conflated with a story about a Pythagorean who revealed irrationality, and writers add imagined details and conjectures. Note: unless quotation marks are used, each claim is summarized. ”32 Aristotle’s words resemble a procedure given later in The Elements. It’s a wonderful argument that we may clarify as follows. Consider a square having sides of length 1 each. By the hypotenuse theorem, its diagonal is then the square root of 2. Is there any segment of length, however small, that can be used to neatly divide both the diagonal and a side of the square?

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