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Re: Math trick? Angst's Theorem??
Posted:
Nov 24, 2012 4:15 AM


"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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