Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ] Topics: [ Previous | Next ]
 Milo Gardner Posts: 1,105 Registered: 12/3/04
Re: Archimedes square root of 3
Posted: Feb 5, 2013 9:23 AM

typos again ... fixed ...

E.J. Dijkerhuis "Archimedes" (1987) 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(would) a more satisfactory solution of the question could possibly look like like?"

Archimedes' method solved (27^1/2)/3 in two steps

1. [(5 + 1/5)^]2/3 = (27 + 1/25)/3

2. [1/25) x 5/52)]/3 = (1/260)/3

such that

(5 + 1/5 + 1/25 - 1/260)/3 = 1351/780

cited in ...

http://planetmath.org/encyclopedia/EgyptianAndGreekSquareRoot.html

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