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Re: Newbie Limit problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg53475] Re: [mg53439] Newbie Limit problem
*From*: Ken Tozier <kentozier at comcast.net>
*Date*: Thu, 13 Jan 2005 03:12:27 -0500 (EST)
*References*: <200501120841.DAA09647@smc.vnet.net> <84C0329D-64EC-11D9-BAD8-000A95B4967A@mimuw.edu.pl>
*Sender*: owner-wri-mathgroup at wolfram.com
On Jan 12, 2005, at 5:51 PM, Andrzej Kozlowski wrote:
> On 12 Jan 2005, at 09:41, Ken Tozier wrote:
>
>> <snip>
>
> You are indeed doing a few things wrong but they are not responsible
> for the lack of result. The first very bad thing you are doing is
> writing 0.5 for the power exponent 1/2. In Mathematica these two
> things
>
> (0.5 and 1/2) are quite different and using the former in
> non-numerical
>
> problems can cause all sorts of weird problems.
OK. didn't know that
> <snip>
>
> But actually, the main points seem to be:
>
> 1) Mathematica just can't do this for general d
>
> 2) While it is easy to prove that the sum is convergent (see below)
> do you have any special reason to expect that there is an explicit
> "closed" formula for it?
I'm self taught so I wasn't aware of the official name of the class of
curves I'm looking at, but have since found that they are called
"trochoids" and they have a whole section devoted to them here:
http://mathworld.wolfram.com/Trochoid.html. Integrals might as well be
written in Martian for all the meaning I get out of them. I find them
impenetrable, so I don't know if the trochoids arc length formula
here: http://mathworld.wolfram.com/CurtateCycloid.html is considered
"closed form" or not.
> Such closed formulas are actually quite rare
> so unless you are lucky neither Mathematica nor anyone else will
> find
> one.
>
> <snip>
Thanks for the help Andrzej. I can see that I need to buckle down and
learn some more advanced math for this one. Integrals (as specified in
the above mathworld page) are incomprehensible to me. I never took
calculus and since the solution involves elliptic integrals, I may have
bitten off more than I can chew. Andrew Wiles used elliptic curves to
prove FLT so elliptics must be REALLY advanced stuff.
Thanks again
Ken
>
>
>
> Andrzej Kozlowski
> Chiba, Japan
> http://www.akikoz.net/~andrzej/
> http://www.mimuw.edu.pl/~akoz/
>
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