Subject: RE: Algorithm question
From: Lindsey, Dr. Charles (clindsey@fgcu.edu)
Date: Sun Apr 02 2000 - 16:07:43 EDT
Although I don't know the Maple algorithm, there is an algebraic identity
that goes back to Arab mathematicians:
sqrt( A - sqrt(B) ) = sqrt( (A+sqrt(A^2-B) ) / 2 ) - sqrt( (A-sqrt(A^2-B) )
/ 2 )
Applying this identity with A=9, B=45 gives your result (after rationalizing
the denominator, which Maple does routinely).
Although this is not a generally useful identity, it can be very useful when
A^2-B is a perfect square, which is the case here.
This is probably a special case of a more general identity that Maple uses
in simplification...
Chuck Lindsey, Ph.D. clindsey@fgcu.edu
Director of General Education
Associate Professor and Program Leader, Mathematics
Florida Gulf Coast University
10501 FGCU Blvd South
Fort Myers, FL 33965-6565
Phone: (941) 590-7168 FAX: (941) 590-7200
http://itech.fgcu.edu/faculty/clindsey
> -----Original Message-----
> From: Kirby Urner [SMTP:pdx4d@teleport.com]
> Sent: Sunday, April 02, 2000 1:11 PM
> To: mathedcc@archives.math.utk.edu
> Subject: Algorithm question
>
>
> I have an expression with a radical under a radical:
>
> sqrt[ 9 - 3 sqrt(5) ]
>
> When I give this to Maple, I get back:
>
> (1/2)sqrt(6)sqrt(5) - (1/2)sqrt(6)
>
> I don't recognize the algorithm being used here,
> although it's not hard to verify the result.
>
> Anyone care to elucidate?
>
> Kirby
> Curriculum writer
>
>
>
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