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Re: Simplification shortcomings?

• To: mathgroup at smc.vnet.net
• Subject: [mg24653] Re: [mg24621] Simplification shortcomings?
• From: BobHanlon at aol.com
• Date: Mon, 31 Jul 2000 09:23:23 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Use FullSimplify

In a message dated 7/28/2000 6:11:02 PM, nitlion at mindspring.com writes:

>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.
>