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Re: Simplification shortcomings?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24666] Re: Simplification shortcomings?
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Fri, 4 Aug 2000 01:18:54 -0400 (EDT)
*Organization*: Universitaet Leipzig
*References*: <8lsutf$27c@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
In[]:=FullSimplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]]
Out[]=0
Regards
Jens
Bob Harris wrote:
>
> Howdy,
>
> I'm a relative novice to Mathematica. While working with it today, I had
> occasion to want to know if a result was equal to (1 + Sqrt[5])/2. The
> result was shown as Sqrt[(3 + Sqrt[5])/2]. After some pancil and paper
> work, I figured out that these two are equal. Or, I should say, that the
> former is one of the values that the latter can have.
>
> I was frustrated in my attempts to get Mathematica to answer that question
> for me. Simplify[(1 + Sqrt[5])/2 - Sqrt[(3 + Sqrt[5])/2]] didn't provide
> any improvement. Calculating this value to many decimal digits showed it
> was near zero (probably close enough that I could have applied the
> techniques shown in Scheinerman's recent article in American Mathematical
> Monthly). The only way I got Mathematica to show the equality was to square
> both numbers; Simplify[((1 + Sqrt[5])/2)^2 - (3 + Sqrt[5])/2] is zero.
>
> Is there any better way to do this? I have some other, more complicated
> numbers that I need to compare.
>
> Thanks,
> Bob Harris
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