Was going to say the same. Also π isn’t infinite. Far from it. it’s not even bigger than 4. It’s representation in the decimal system is just so that it can’t be written there with a finite number of decimal places. But you could just write “π”. It’s short, concise and exact.
That doesnt make a difference. You can find the exact circumference of a circle, you just cant express it in the decimal system as a number (thats why we have a symbol for it so you can still express the exact value)
“Find” not “define”
Putting things in base 10 is also a definition. Digits aren’t special.
Was going to say the same. Also π isn’t infinite. Far from it. it’s not even bigger than 4. It’s representation in the decimal system is just so that it can’t be written there with a finite number of decimal places. But you could just write “π”. It’s short, concise and exact.
Can pi be expressed with a finite amount of digits in another number system?
I don’t think there’s any technical reason we can’t count in base pi
Well we need an integer base number system…
“A base is usually a whole number bigger than 1, although non-integer bases are also mathematically possible.”
https://simple.m.wikipedia.org/wiki/Base_(mathematics)
But it makes life harder
Not if you’re mainly interested in counting multiples of pi.
I’m pretty happy with being able to write integers in a finite number of digits. Wouldn’t want to give that up.
How about a pi based system, then pi is 1.
Base π would be 10
You’re correct.
For reference: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration
Not sure where you’re going with the decimal thing. Pi had infinite digits in any integer base because it’s irrational.
That doesnt make a difference. You can find the exact circumference of a circle, you just cant express it in the decimal system as a number (thats why we have a symbol for it so you can still express the exact value)