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

• To: mathgroup at smc.vnet.net
• Subject: [mg20027] Re: [mg19976] Out[1]=((5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) == 1/2 ???
• From: "Mark E. Harder" <harderm at ucs.orst.edu>
• Date: Sat, 25 Sep 1999 02:40:51 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Patrick,
Further Food For Thought:

In[4]:=Sqrt[5]/20 ==Sqrt[5.]/20
Out[4]= True

Judging from your error msg. (which reproduced in my Mathematica 3.0.2, Win
NT system), Mathematica fails when it tries to evaluate Sqrt[5] in finite
precision and make the comparison in your expression, but it will do that in
the above.  Using N[ expr, \$MachinePrecision], however, is error free:

In :=N[( (5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) ,\$MachinePrecision]
Out:=0.5
In:=N[( (5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) ,\$MachinePrecision]== 1/2
Out:=True

But I'm not sure just why or how it makes these decisions.
-mark

From: Patrick McLean <p_mclean at postoffice.utas.edu.au>
To: mathgroup at smc.vnet.net
Subject: [mg20027] [mg19976] Out[1]=((5-Sqrt[5])/20 + (5+Sqrt[5])/20 ) == 1/2 ???

>Can any one explain this behaviour???
>
>hilbert% math
>Mathematica 3.0 for Solaris
> -- Terminal graphics initialized --
>
>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
>
>In[2]:=
>
>--
>Patrick McLean
>
>No news is good news...
>

```

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