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Topic: Archimedes square root of 3
Replies: 8   Last Post: Feb 5, 2013 9:23 AM

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 Milo Gardner Posts: 1,105 Registered: 12/3/04
Re: Archimedes square root of 3
Posted: Feb 4, 2013 4:29 PM

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?"

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.

Date Subject Author
1/16/13 Milo Gardner
1/16/13 Milo Gardner
1/17/13 Milo Gardner
1/20/13 Milo Gardner
1/24/13 Milo Gardner
2/4/13 Milo Gardner
2/4/13 Milo Gardner
2/4/13 Milo Gardner
2/5/13 Milo Gardner