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