JT
Posts:
1,215
Registered:
4/7/12


Re: sqrt(x) without approximation?
Posted:
Feb 10, 2013 2:46 AM


On 10 Feb, 00:32, forbisga...@gmail.com wrote: > On Saturday, February 9, 2013 1:30:25 PM UTC8, Virgil wrote: > > In article > > <98c9f2d8e09f4cc3aedad51f831b8...@k14g2000vbv.googlegroups.com>, > > JT <jonas.thornv...@gmail.com> 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. > > > No and no! > > > While sqrt(N) for nonsquare N, can be approximated in standard > > notations, I do not see that there can be any analog to digits to the > > right of a decimal point for your NyaN numbers. > > In base sqrt(n), n is expressed as 100. I'm not sure how to add the > natural number 1 to a number in a fractional base system where the > base is > 1. I would presume that in base 2.5(decimal), 2 + 1 = 10.111..., > though I'm not quite sure.
What base are you writing 2,5 equal 10.111... you totally lost me here, can you write out the multiples so i see what is going on? Since number systems is represenational you can write any decimal on the form 0,000512 =10^6*512 this is also true for anybase, so if we want to write 2,5 in ternary it will be 2,12 since 12 = 5 =1*3+2*1 in ternary. And we can use this fact for anybase as long we keep track of the positional multiple. Ternary base 1,3,9,27,81 and so on.

