Date: Mar 23, 2013 7:14 AM
Author: JT
Subject: Re: Is there any webpage or math program that can write fracitons,<br> numbers into bijective enumeration?

On 22 mar, 16:23, JT <jonas.thornv...@gmail.com> wrote:
> On 22 mar, 16:20, JT <jonas.thornv...@gmail.com> wrote:
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> > On 19 mar, 09:36, JT <jonas.thornv...@gmail.com> wrote:
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> > > On 19 mar, 07:18, JT <jonas.thornv...@gmail.com> wrote:
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> > > > Surely someone must found it interesting enough to implement it?
> > > > A generic basechanger working in anybase for bijective encoded numbers
> > > > would be nice.

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> > > Could anyone gifted? mathematician help me encode the positive numbers
> > > upon the following bijective (NyaN) form?

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> > > Binary      1=.2   1/2=.1  2/2=.2   1/4=.(1)1    2/4=.(1)2
> > > Ternary     1=.3   1/3=.1  2/3=.2   1/9=.(1)1    2/9=.(1)2  1/27=.
> > > (2)1    2/27=.(2)2   1/81=.(3)1   2/81=.(3)2
> > > Quaternary  1=.4   1/4=.1  2/4=.2   1/16=.(1)1   2/16=.(1)2
> > > Quinary     1=.5   1/5=.1  2/5=.2   1/25=.(1)1   2/25=.(1)2
> > > Senary      1=.6   1/6=.1  2/6=.2   1/36=.(1)1   2/36=.(1)2
> > > Septenary   1=.7   1/7=.1  2/7=.2   1/49=.(1)1   2/49=.(1)2
> > > Octal       1=.8   1/8=.1  2/8=.2   1/64=.(1)1   2/64=.(1)2
> > > Nonary      1=.9   1/9=.1  2/9=.2   1/81=.(1)1   2/81=.(1)2
> > > Decimal     1=.A   1/10=.1 2/10=.2  1/100=.(1)1  2/100=.(1)2

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> > > Ternary maybe the best choice for checking out the results of your
> > > generic recursive base implementation since it fairly easy to follow
> > > what is goin on.
> > > 1/3       = .1
> > > 2/3       = .2
> > > 1/9       = .(1)1
> > > 2/9       = .(1)2
> > > 1/27      = .(2)1
> > > 2/27      = .(2)2
> > > 1/81      = .(3)1
> > > 2/81      = .(3)2

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> > > And for the Naturals
> > > 1   =1
> > > 2   =2
> > > 3   =3
> > > 4   =11 3+1
> > > 5   =12 3+2
> > > 6   =13 3+3
> > > 7   =21 6+1
> > > 8   =22 6+2
> > > 9   =23 6+3
> > > 10  =31 9+1
> > > 11  =32 9+2
> > > 12  =33 9+3
> > > 13  =111 9+3+1
> > > 14  =112 9+3+2
> > > 15  =113 9+3+3
> > > 16  =121 9+6+1
> > > 17  =122 9+6+2
> > > 18  =123 9+6+3
> > > 19  =131 9+9+1
> > > 20  =132 9+9+2
> > > 21  =133 9+9+3

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> > > Here is a start for your attempt to make an algorithm that will encode
> > > any decimal number with decimal parts into anybase,(i can't quite get
> > > it right but for you guys it should be pieceof a cake).
> > > It is maximum two lines of code.http://www.anybase.co.nf/

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> > Regarding changing bases of reals like i do in script above, there is
> > separate the wholenumber part from the decimal part but of course if
> > the number is 1111,1111 i could reencode it to 11111111 * (10^(-4)) =
> > 1111,1111 but then one must deal with the  base power.

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> And then the base changing function would work for any real, (it is
> right now too) but maybe not that aestethical from  a math perspective?

http://www.youtube.com/watch?v=WKhh71qX0J4