Re: Help Define a Constant I get from Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg118563] Re: Help Define a Constant I get from Mathematica
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Tue, 3 May 2011 05:45:04 -0400 (EDT)
Your 5,000 iterations are overkill, since it only takes 14 iterations (or so) to get the same limit: l = RandomReal[{0.044685172, 1}, WorkingPrecision -> 200]; list = FixedPointList[FromContinuedFraction@Convergents[#, 100] &, l, 50, SameTest -> (Abs[#1 - #2] < 10^-30 &)]; -1 + Length@list N[Last@list, 30] 14 0.555753104278045912445405869381 Bobby On Mon, 02 May 2011 05:53:41 -0500, Marvin Burns <marburns at umail.iu.edu> wrote: > Can you help define this constant I get from Mathematica? > > Here is the code I use: > > Table[{N[l = RandomReal[{0.044685172, 1}, WorkingPrecision -> 200]], > > Table[c = Convergents[l, 100]; > > l = FromContinuedFraction[c], {n, 1, 50}]; > > N[l, Floor[30]]}, {m, 1, 100}] // TableForm > > > > I get c=0.55575310427804591244540586938..., and no other value, every > time I > run it! > > I know basically Mathematica is using the convergents of a real number in > the domain as terms to form a generalized continued fraction. Then it > uses > the convergents of that generalized continued fraction as terms to form > another generalized continued fraction, and continues to repeat this > process > until it gets to where I told it to stop. Strangely, initial > input<0.044685172 seems to have output that is extremely sensitive to > variations. For example, .04468513845124463 gives 3.2765033850144244631 > but > .044685138451244635 gives 0.55575310427804591245, and then > .044685138451244635105 gives 3.276503385014424463 again. > > There must be more rigorous way to define it. > > Do you think it deserves a name? What would be a good name for it? > > Marvin Ray Burns > > Original investigator of the MRB constant (I didn't name that.) -- DrMajorBob at yahoo.com