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MathGroup Archive 2005

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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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