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SRH
2013-Feb-09, 06:59 AM
Using ternary (base 3) mathematics, how would one write out Tau (2 pi)?

Thanks!

cjl
2013-Feb-09, 07:02 AM
http://www.wolframalpha.com/input/?i=2*pi+in+base+3

Jens
2013-Feb-09, 10:37 AM
I may be a bit mathematically challenged, but what is tau? Also, this may be silly, but isn't pi written pi in whatever base you are using?

caveman1917
2013-Feb-09, 12:03 PM
I may be a bit mathematically challenged, but what is tau?

Tau has been proposed as a constant in addition to pi because it would simplify writing down some formulae as you get 2pi appearing a lot. It hasn't really been adopted, just a proposal.


Also, this may be silly, but isn't pi written pi in whatever base you are using?

Sure, but its expansion changes depending on the base.

Jens
2013-Feb-09, 12:12 PM
Sure, but its expansion changes depending on the base.

By expansion, do you mean the 3.14 etc part? If so, then of course you're right that it changes. But if you're only required to translate pi, I think it would be the same whatever the base. Of course, in binary, 2pi would have to be written 10 pi.

Strange
2013-Feb-09, 12:54 PM
Of course, http://www.wolframalpha.com/input/?i=2*pi+in+base+pi gives a nice simple representation of the value.

caveman1917
2013-Feb-09, 12:56 PM
By expansion, do you mean the 3.14 etc part? If so, then of course you're right that it changes. But if you're only required to translate pi, I think it would be the same whatever the base. Of course, in binary, 2pi would have to be written 10 pi.

Yes the number pi remains the same, all that changes is the way you write it out. But i think it was clear from the OP question that he wanted the expansion in base 3, so i'm not sure what exactly your point is?

swampyankee
2013-Feb-09, 02:52 PM
Using bc (it's on all computers that use a real O/S; for everybody else, you can get it from cygwin.com), it's 20.021122102221021122011222221220222211000021

All you have to do is
bc -l
obase=3
2*4*a(1)

quit

obase sets the output base
a(1) is the arctangent of 1 radian, which is pi/4

In base 2, tau is 110.0100100001111110110101010001000100001011010001 100001000110100101010

base 4: 12.1020133231110101002310120101221111
base 5: 11.12014434112242032303300313312
base 16: 6.487ED5110B4611A55

grapes
2013-Feb-09, 02:57 PM
Of course, http://www.wolframalpha.com/input/?i=2*pi+in+base+pi gives a nice simple representation of the value.20 :)

Can't get much simpler than that!

HenrikOlsen
2013-Feb-09, 03:15 PM
20 :)

Can't get much simpler than that!
In base 2pi it's 10 which is about as simple and useless as you can get.