Virgil
Posts:
4,486
Registered:
1/6/11
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Re: sqrt(x) without approximation?
Posted:
Feb 10, 2013 4:24 AM
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In article
<b635a1d7-4f6a-4b36-b941-01ad0fed013a@dp10g2000vbb.googlegroups.com>,
JT <jonas.thornvall@gmail.com> wrote:
> On 10 Feb, 02:22, Wally W. <ww8...@aim.com> wrote:
> > On Sat, 9 Feb 2013 02:40:56 -0800 (PST), JT wrote:
> > >Is there always such a base for any N that we can write sqrt(N)
> > >without approximation? Would it matter if we use NyaN or standard
> > >bases.
> >
> > What is NyaN?
>
> It is a concept of new naturals working in anybase(Nya N swedish), it
> is written out without zeros.
> BASE 3 BELOW
> Dec = NyaNTern=StandardTern
> 1 =1 01
> 2 =2 02
> 3 =3 10
> 4 =11 3+1 11
> 5 =12 3+2 12
> 6 =13 3+3 20
> 7 =21 6+1 21
> 8 =22 6+2 22
> 9 =23 6+3 100
> 10 =31 9+1 101
> 11 =32 9+2 102
> 12 =33 9+3 110
> 13 =111 9+3+1 111
> 14 =112 9+3+2 112
> 15 =113 9+3+3 120
> 16 =121 9+6+1 121
> 17 =122 9+6+2 122
> 18 =123 9+6+3 200
> 19 =131 9+9+1 201
> 20 =132 9+9+2 202
> 21 =133 9+9+3 210
>
> Below ternary fractions in NyaN
> Paragraphs for empty preceding
> entrys to keep track of multiple * bas (Ternary=1,3,9,27,81....)
>
> Fractions = NyaN ternary fraction
> 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 ...
How does one do 1/2 in NyaN ternary?
And why is Nyan 1/9 = .(1)1 any better than base 3 standard 1/9 = .01
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