TIB: 10 in base pi (was Re: Real number to string)
[Prev][Next][Index][Thread]
TIB: 10 in base pi (was Re: Real number to string)
>From: Lloyd Hugh Allen <lha2@home.com>
>Reply-To: ti-basic@lists.ticalc.org
>To: ti-basic@lists.ticalc.org
>Subject: Re: TIB: Real number to string
>Date: 2000-09-17 08:07:54 -0400
>The question is: if pi base ten is 3.14159...etcetc..., what is ten base
>pi?
Excellent question.
It's quite simple, really. All you need to do is set up a place value
system pi^2, pi, 1, 1/pi, 1/pi^2, 1/pi^3, etc. We'll need only the digits
0-3.
Now, the calculations. It's just like converting to an integer base, except
that we have to divide by irrational numbers.
10/piČ = 1 with remainder 0.130 395 598 9
(pi, 1, and 1/pi places are zero)
0.130 395 598 9/(pi^-2)=1 with remainder 0.029 074 415 3
(pi^-3 digit is zero)
0.029 074 415 3/(pi^-4)=2 with remainder 0.008 542 450 8
0.008 542 450 8/(pi^-5)=2 with remainder 0.002 006 923 5
0.002 006 923 5/(pi^-6)=1 with remainder 0.000 966 762
0.000 966 762/(pi^-7)=2 with remainder 0.000 304 575
0.000 304 575/(pi^-8)=2 with remainder 0.000 093 794
0.000 093 794/(pi^-9)=2 with remainder 0.000 026 7
etc.
Therefore, the base-pi representation of 10 is 10.010 221 222...
The calculations are rather tedious by hand but I have a program capable of
converting a base-10 number to any base, even an irrational one. You can
find it at http://www.ticalc.org/pub/83/basic/math/baseconv4.zip
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
Share information about yourself, create your own public profile at
http://profiles.msn.com.