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Topic: Math trick? Angst's Theorem??
Replies: 12   Last Post: Dec 4, 2012 8:33 AM

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Lord Androcles, Zeroth Earl of Medway

Posts: 28
Registered: 11/6/12
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

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Lord Androcles, Zeroth Earl of Medway











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