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Re: Archimedes square root of 3
Posted:
Feb 4, 2013 4:29 PM


Reply
E.J. Dijkerhuis "Archimedes" page 435 discussed
(27^1/2)/3 in terms of a continuing fraction series
cited 3^1/2, 26/15, 265/153, 1351/780
followed by
"... what a more satisfactory solution of the question could possibly look like like?"
how about ...
1. (5 + 1/50^2 = (27 + 1/25)/3
2. [(5 + 1/5 + 1/25X 52/5 = 1/260}/3
such that
(5 + 1/5  1/260}/3 = 1351/780
Q.E.D.



