PI IS EXACTLY 3.2 ..mathematicians collectively gasp

The only numbers of Pi I have memorized are 3.14159
 
3.14159265358979323 is all I have memorized now. I had 50 digits memorized at the end of last year. My calc teacher offered everyone extra credit if they could write 50 digits accurately without any aid.
 
delusional said:
It equals 22/7 if that makes you feel better. 22/7 is actually the exact number though.
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Clearly that follows from it being irrational, right?

Now that I think about it I remember there being a Putnam problem of evaluating the integral equal to 22/7 - Pi.
 
ericms said:
Clearly that follows from it being irrational, right?

Now that I think about it I remember there being a Putnam problem of evaluating the integral equal to 22/7 - Pi.
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Ya I guess i'm wrong.

Pi equals exactly 10 in base pi though. :O
 
Don't you need to use a real integer as the base of any counting system? I don't think base pi is possible unless you reevaluated the value of 1... which doesn't make sense, because 1 is already defined.
 
Dan said:
Don't you need to use a real integer as the base of any counting system? I don't think base pi is possible unless you reevaluated the value of 1... which doesn't make sense, because 1 is already defined.
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For counting, yes. But the idea can naturally apply to any base.

wxy.z (base b) means w * b^2 + x * b^1 + y * b^0 + z * b^-1

In base 10, you have w hundreds, x tens, y ones, and z tenths.
In base pi, you have w 'pi^2's, x 'pi's, y ones, and z '1/pi's.

So 10 (base pi) = 1 * pi^1 + 0 * pi^0 = 1 * pi + 0 * 1 = pi + 0 = pi.

It's not good for counting because you'll never get enough ones to equal pi, or enough pi's to equal pi^2, so you end up needing a "digit" for each integer (including negatives).
 
Qhartb said:
For counting, yes. But the idea can naturally apply to any base.

wxy.z (base b) means w * b^2 + x * b^1 + y * b^0 + z * b^-1

In base 10, you have w hundreds, x tens, y ones, and z tenths.
In base pi, you have w 'pi^2's, x 'pi's, y ones, and z '1/pi's.

So 10 (base pi) = 1 * pi^1 + 0 * pi^0 = 1 * pi + 0 * 1 = pi + 0 = pi.

It's not good for counting because you'll never get enough ones to equal pi, or enough pi's to equal pi^2, so you end up needing a "digit" for each integer (including negatives).
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But there is no requirement that b amount of the 1s column must add up to b^1? So in binary, you don't have the choice or writing "2" as 10 or 02, because you can't use the digit 2. The highest possible value of one column has to be one less than the value of the next column. In base 10, after 9, you jump columns to 10. But that is impossible in base pi because pi isn't an integer, you would count 1,2,3.... 10? How is the rightmost column counted?
 
PI is exactly 3 peanuts over a rabbit problem solved now move on
 
3 = white shoe

And you're an idiot if you don't believe that
 
Dan said:
But there is no requirement that b amount of the 1s column must add up to b^1? So in binary, you don't have the choice or writing "2" as 10 or 02, because you can't use the digit 2. The highest possible value of one column has to be one less than the value of the next column. In base 10, after 9, you jump columns to 10. But that is impossible in base pi because pi isn't an integer, you would count 1,2,3.... 10? How is the rightmost column counted?
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That's why base pi not good for counting. It's not good for much of anything, actually.

(Because I may need to talk about "digits" other than the standard 0-9, I'm going to place brackets around each digit. Ex. "eleventy one" = [11][1], while "one hundred twenty four" = [1][2][4].)

In decimal, we usually don't call numbers things like "eleventy one," because the tens place of the eleven can be "carried" into the hundreds place, making "one hundred eleven". If we don't worry about carrying and allow any number as a digit, adding is easy:

[1][3][2] + [3][8][8] = [4][11][10]
So one hundred thirty two plus three hundred eighty eight is four hundred eleventy ten, just by adding the digits. That works even in base pi.

Similarly, subtraction in any base will work by subtracting digits, you might just get ugly negative digits in your result.

The part that doesn't work in base pi is taking digits that are too big and carrying them into higher places, putting the number back in a form that's easy to understand. (And a canonical form that makes it easy to tell when two numbers are the same. It's not easy to see that eleven thousand eleven hundred is the same number as twelve thousand one hundred, for example.)

In base ten:
[4][11][10] = [4 + 1][1 + 1][0] = [5][2][0]

In base pi:
[4][11][10] = 4 pi^2 + 11 pi + 10, and that's as simple as you can make it.
 
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