RE: mathematical concepts=="irrational numbers"

From: bivalve (
Date: Thu Sep 04 2003 - 11:43:33 EDT

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    >"Irrational" numbers...were thus named b/c they did not meet the Greek standard of "rational" mathematics--ie, they could not be written as the quotients of whole numbers. They were not thereby related to the harmonic ratios in music (recall that music was once a branch of mathematics). <

    Actually, irrational numbers do turn up from harmonic ratios in music, if you want to make an instrument that can play fixed notes that sound good in any key (e.g., a keyboard instrument). The ratios between different notes in the scale adjusted to the ideal for one key do not quite match what is needed for another key. This problem did not arise for the ancient Greeks, but it did pose difficulties for early piano makers.

    As a discussion a little while ago noted, the Fibonacci series turns up in nature. The golden ratio, an irrational number, is closely linked with the Fibonacci series.

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