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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