Re: Leibniz Definition Of Pi Not In 5.0.0?
- To: mathgroup at smc.vnet.net
- Subject: [mg43219] Re: Leibniz Definition Of Pi Not In 5.0.0?
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Wed, 20 Aug 2003 22:25:10 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Tuesday, August 19, 2003, at 01:53 PM, H. Burke Jensen wrote:
> $Version: 5.0 for Microsoft Windows (June 10, 2003)
>
> $MachineType: PC
>
> $OperatingSystem: WindowsNT
>
>
>
> Hello MathGroup,
>
>
>
> Does Mathematica 5.0.0 not recognize the Leibniz definition of Pi
> [Ref.1]?
> This was recognized in Mathematica 3.0.1 and reported to WRI.
>
>
>
> In[1]:=
>
> \!\(\[Pi]\/4 === \[Sum]\+\(n = 1\)\%\[Infinity] If[
>
> EvenQ[n] \[Equal] True, \(-\(1\/\(2 n - 1\)\)\), 1\/\(2 n -
> 1\)]\)
>
>
>
> Sum::div: Sum does not converge.
>
>
>
> Sum::div: Sum does not converge.
>
>
>
> Out[1]=
>
> False
>
>
>
> References:
>
> [1] Martin, George E., The Foundations of Geometry and the
> Non-Euclidean
> Plane, Springer, 1975, p. 157-158.
>
>
>
> Thank you,
>
> -H. Burke Jensen
>
> hbj at ColoradoKidd.com
>
> The Colorado Kidd®
>
> www.ColoradoKidd.com
>
>
>
This works fine:
In[20]:=
Sum[(-1)^(n + 1)*(1/(2*n - 1)), {n, 1, Infinity}]
Out[20]=
Pi/4
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/