Re: Re: Leibniz Definition Of Pi Not In 5.0.0?
- To: mathgroup at smc.vnet.net
- Subject: [mg43319] Re: [mg43264] Re: Leibniz Definition Of Pi Not In 5.0.0?
- From: Dr Bob <drbob at bigfoot.com>
- Date: Sun, 24 Aug 2003 04:55:22 -0400 (EDT)
- References: <bht3v3$n4n$1@smc.vnet.net> <200308231208.IAA25101@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
Mathematica works by simplifying patterns, and the If[...] construct in your example isn't recognized as the same as the other summand, with powers of -1. It's easy to say that Mathematica SHOULD recognize it, but at what cost? How many different simpler expressions can be disguised with If, Which, and Switch? Bobby On Sat, 23 Aug 2003 08:08:41 -0400 (EDT), H. Burke Jensen <hbj at ColoradoKidd.com> wrote: > Thank you All for the better code! > > My question still stands though regarding why using this method the Sum > is > incorrectly identified. I'm trying to figure out the internal thinking > Mathematica does to discover where the difference drives an incorrect > identification. Any ideas? > > Thank you again, > -H. Burke Jensen > hbj at ColoradoKidd.com > The Colorado Kidd® > www.ColoradoKidd.com > > "H. Burke Jensen" <hbj at ColoradoKidd.com> wrote in message > news:bht3v3$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 > > -- majort at cox-internet.com Bobby R. Treat
- References:
- Re: Leibniz Definition Of Pi Not In 5.0.0?
- From: "H. Burke Jensen" <hbj@ColoradoKidd.com>
- Re: Leibniz Definition Of Pi Not In 5.0.0?