Re: Leibniz Definition Of Pi Not In 5.0.0?
- To: mathgroup at smc.vnet.net
- Subject: [mg43299] Re: Leibniz Definition Of Pi Not In 5.0.0?
- From: "H. Burke Jensen" <hbj at ColoradoKidd.com>
- Date: Sun, 24 Aug 2003 04:54:57 -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
Thanks again for the responses!
Sum[f, {i, imax}]
The documentation says "If a sum cannot be carried out explicitly by adding
up a finite number of terms, Sum will attempt to find a symbolic result. In
this case, f is first evaluated symbolically."
So, am I correct in saying that in the function Sum, one must use an
evaluated form of f (function) in order to properly use the iteration
variable (i) for the Sum?
If this is true, this is a subtle point of Sum I did not grasp before. I had
thought since it was wrapped in Sum[...] that a more liberal use of the
iteration symbol (i) was allowed. I hope this helps others!
Trace[\[Pi]/4===Sum[If[EvenQ[n]==True,-1/(2n-1),1/(2n-1)], {n, 1,
Infinity}]][[2,5]]
"\[UpArrow] Mathematica algorithm evaluation first alters f versus does not
\[DownArrow]"
Trace[Sum[(-1)^(n + 1)*(1/(2*n - 1)), {n, 1, Infinity}]][[1]]
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