Date: Feb 4, 2013 4:29 PM
Author: Milo Gardner
Subject: Re: Archimedes square root of 3

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.