Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: Leibniz Definition Of Pi Not In 5.0.0?

• To: mathgroup at smc.vnet.net
• Subject: [mg43264] Re: Leibniz Definition Of Pi Not In 5.0.0?
• From: "H. Burke Jensen" <hbj at ColoradoKidd.com>
• Date: Sat, 23 Aug 2003 08:08:41 -0400 (EDT)
• References: <bht3v3$n4n$1@smc.vnet.net>
• Reply-to: "H. Burke Jensen" <hbj at ColoradoKidd.com>
• Sender: owner-wri-mathgroup at wolfram.com

Thank you All for the better code!

My question still stands though regarding why using this method the Sum is
incorrectly identified. I'm trying to figure out the internal thinking
Mathematica does to discover where the difference drives an incorrect
identification. Any ideas?

Thank you again,
-H. Burke Jensen
hbj at ColoradoKidd.com
The Colorado Kidd®
www.ColoradoKidd.com

"H. Burke Jensen" <hbj at ColoradoKidd.com> wrote in message
news:bht3v3$n4n$1 at smc.vnet.net...
$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

• Follow-Ups:
  • Re: Re: Leibniz Definition Of Pi Not In 5.0.0?
    • From: Dr Bob <drbob@bigfoot.com>