Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Math Forum
»
Discussions
»
sci.math.*
»
sci.math
Topic:
Is there any webpage or math program that can write fracitons, numbers into bijective enumeration?
Replies:
68
Last Post:
Apr 8, 2013 11:40 PM



JT
Posts:
1,434
Registered:
4/7/12


Re: Is there any webpage or math program that can write fracitons, numbers into bijective enumeration?
Posted:
Mar 25, 2013 3:48 AM


On 25 mar, 04:51, david petry <david_lawrence_pe...@yahoo.com> wrote: > On Thursday, March 21, 2013 2:52:56 AM UTC7, JT wrote> > > Ternary NyaN format > > > > > 1=1 {1} > > > 2=2 {1,1} > > > 3=3 {1,1,1} > > If I search for "NyaN" in Google, I get links to some YouTube cat video. If I search for "Nyan fractions" I get links to your article. > > So what does "NyaN" mean?
Ny or nya means new in swedish and N is the positive integers, the NyaN algorithm encode the positive integers into a a bijective? zeroless basesystems (anybase). I constructed the algorithm that can convert any positive real into NyaN format, see below.
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 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 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



