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.
And by that definition 0.1 is also infinite… My computer can’t write that with a finite amount of digits in base 2, which it uses internally.
So… I’m crying salty tears, too.
[Edit: And we don’t even need transcendental numbers or other number systems. A third also doesn’t have a representation. So again following the logic… you can divide a cake into 5 pieces, but never into 3?!]
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.
And by that definition 0.1 is also infinite… My computer can’t write that with a finite amount of digits in base 2, which it uses internally.
So… I’m crying salty tears, too.
[Edit: And we don’t even need transcendental numbers or other number systems. A third also doesn’t have a representation. So again following the logic… you can divide a cake into 5 pieces, but never into 3?!]
Can pi be expressed with a finite amount of digits in another number system?
How about a pi based system, then pi is 1.
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You’re correct.
For reference: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration
Possible, but then the diameter would be an irrational number
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.
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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)