Leibniz Definition Of Pi Not In 5.0.0?
- To: mathgroup at smc.vnet.net
- Subject: [mg43213] Leibniz Definition Of Pi Not In 5.0.0?
- From: "H. Burke Jensen" <hbj at ColoradoKidd.com>
- Date: Wed, 20 Aug 2003 22:25:01 -0400 (EDT)
- Reply-to: "H. Burke Jensen" <hbj at ColoradoKidd.com>
- Sender: owner-wri-mathgroup at wolfram.com
$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