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I have a question, is it possible to use $\pi$ as a single unit like we get $3,14$ as $1$, and use it to develope a new numerical basis based on $\pi$ in which number $2$ will be $\pi \cdot 2$ , and if so does it exist? in this new basis can $\pi$ has an exact amount?

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closed as unclear what you're asking by Lord Shark the Unknown, TheSimpliFire, Dietrich Burde, Blue, futurebird Mar 21 '18 at 22:32

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ See this duplicate. $\endgroup$ – Dietrich Burde Mar 21 '18 at 19:48
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    $\begingroup$ Possible duplicate of What would a base $\pi$ number system look like? $\endgroup$ – Blue Mar 21 '18 at 19:49
  • $\begingroup$ "In this new basis can $pi$ have an exact amount?" The answer is yes because from your definition $\pi=1_{\pi}$ $\endgroup$ – KKZiomek Mar 21 '18 at 19:49
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    $\begingroup$ @KKZiomek $\pi$ has an "exact amount" also in basis $10$. $\endgroup$ – Dietrich Burde Mar 21 '18 at 19:49
  • $\begingroup$ Also worth noting that a similar "system" is used and is useful. There's a thing called the diameter tape, basically you measure something circular with it, and it gives you automatocally the diameter of that object $\endgroup$ – KKZiomek Mar 21 '18 at 19:51
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Yes. Non-integer bases can be used to represent numbers. See https://en.wikipedia.org/wiki/Non-integer_representation#Base_%CF%80 But $\pi$ is $\pi$ (and is an exact number) no matter what, so I don’t understand the last part of your question. In base $\pi$, the representation of $\pi$ (assuming you use the usual single digits) will be $10$, but that doesn’t make $\pi$ equal to “ten.” It’s still a little bigger than three.

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It kind of depends...

There's no problem in having base $\pi$ in a positional number system, but it's hard to find $\pi$ different symbols, so most (all?) numbers will have multiple representations.

And obviously $\pi$ will representable as $10$ in that system, if that's what you mean by "has an exact amount".

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