So Basepi got me thinking...


#1

I just learned about bases in school and I’m thinking about how base Pi would work. And if it would work.

Saw this: http://forums.randi.org/archive/index.php/t-5262.html

So let’s think.

If it was base 3, then it would just be

1,2,10,11,12,20,21,22,100…

But if Pi includes 1 through 9, but you can only count to 3.14159… So
1,2… AHG. I can’t understand…


#2

No, you can easily express any integer with base three. You can also express any real number with base three (or any integer base where the base is ≥ 2), but each base has certain values that it can’t express as cleanly. (Think about 1/3 in base ten: 0.3333 repeating.) The main difference between base ten and base three is that you are limited to digits 0-2. Here are a few examples.

[tr][td]Base 10 [/td][td]Base 3[/td][/tr]
[tr][td]2[/td][td]2[/td][/tr]
[tr][td]10[/td][td]101[/td][/tr]
[tr][td]21[/td][td]210[/td][/tr]

or in general, every number in base three is expressed in the form:

X*30 + … + X*30 + X*30 + X*30

No, as previously shown, you can count to any number. In general the form would be:

X0 + … + X0 + X0 + X0

The peculiarity with base π is that all integers become very messy.


#3

What I was saying was that you can only use(like you said) 0-2, therefore you count, 0,1,2,10,11,12,20,21,22,100… I used the incorrect wording when I said you could only count to Pi.

So like for binary 6 base 10 would be 110

Is that incorrect?

Wait a second, if I take lets say the number 6 and divide it by 3.141, then divide the remainder by 1, that mean 6 in base pi is around 12.859…… I get it now. But counting would just be really hard.


#4

it doesn’t actually make sense, pi includes digits that are higher than pi.


(Former National 4A Champion) #5

saying base pi does not necessarily mean a counting system. It could mean pi^x which an exponent with base pi; or, it could be log base pi.


#6

That was my question.


#7

That is not a problem because pi can be written with any set of digits by writing it in different bases. It doesn’t have to have digits that are larger than pi. It does in base 10 because base 10 has digits that are larger than pi, but in base 2, for example, pi would be 11.0010010… All the digits would be 1 or 0. In base pi, pi would just be 10, and any other number would only use the digits 0-3.

Yes, but you still have the decimal part written in base 10, so once you convert that as well it comes out to 12.220…


#8

Oh I get it, because Pi is in base ten, you need to put Pi in base Pi, which would be 1. Aha.