Simplification shortcomings?

*To*: mathgroup at smc.vnet.net*Subject*: [mg24621] Simplification shortcomings?*From*: Bob Harris <nitlion at mindspring.com>*Date*: Fri, 28 Jul 2000 17:23:59 -0400 (EDT)*Organization*: MindSpring Enterprises*Sender*: owner-wri-mathgroup at wolfram.com

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