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Re: Out[1]=((5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) == 1/2 ???

• To: mathgroup at smc.vnet.net
• Subject: [mg20007] Re: Out[1]=((5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) == 1/2 ???
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 25 Sep 1999 02:40:38 -0400
• Organization: Universitaet Leipzig
• References: <7se6fk$qsc@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

H Patrick,

you ask is ( (5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) 

equal to 1/2. This should be True. To evaluate this Mathematica
don't call Together[]. It find that

 NumericQ[( (5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) ]

yield True and try to evaluate it numerical :-(

This gives the message from the numerical evaluation.

Hope that helps
  Jens

Patrick McLean wrote:
> 
> Can any one explain this behaviour???
> 
> 
> In[1]:=   ( (5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) == 1/2
> 
> $MaxExtraPrecision::meprec:
>    $MaxExtraPrecision = 50. reached while evaluating
>       1    5 - Sqrt[5]   5 + Sqrt[5]
>     -(-) + ----------- + -----------. Increasing the value of
>       2        20            20
>      $MaxExtraPrecision may help resolve the uncertainty.
> 
>         5 - Sqrt[5]   5 + Sqrt[5]    1
> Out[1]= ----------- + ----------- == -
>             20            20         2

> Patrick McLean
> 
> No news is good news...