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)
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.
Not true. If you define the circumference in terms of pi, you can define the circumference exactly.
“Find” not “define”
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)
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
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.