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Re: Math trick? Angst's Theorem??
Posted:
Nov 24, 2012 4:15 AM
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"Existential Angst" wrote in message
news:50b081e1$0$9827$607ed4bc@cv.net...
Try this on a calculator/spreadsheet:
Take sq rt of 10, to as many places as poss.. Then take recip. What do you
see?
For the calculationally lazy: 3.162277660168 --> .3162277660168... !!!!
Weird coincidence? Predictable??
Angst's Theorem??
--
EA
================================================
Predictable.
Take sqrt(2) = 1.414...
reciprocal = 0.707... (= 1.414.../2)
Try this on a spreadsheet:
sqrt(2) = 1.414...
subtract 1 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
reciprocal = 2.414...
subtract 2 = 0.414...
sqrt(2) = 1 + 1/(2 + 1/(2 + 1/(2 + ...)))
http://en.wikipedia.org/wiki/Generalized_continued_fraction
-- This message is brought to you from the keyboard of
Lord Androcles, Zeroth Earl of Medway
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