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How would the following formulars change if we use a base 6 arabic number system?

  • quadratic formula (=midnight formula)

  • Einsteins e=mc^2

  • pi

  • circle A=pi*r^2

It would be counted like this: 0 1 2 3 4 5 10 11 12 13 14 15 20 21 22 23 24 25 30 31 32 33 34 35 40 41 42 43 44 45 50 51 52 53 54 55 100 101....

Squareoot
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    First of all, $\pi$ is not a formula, it is a number. Secondly, formulas in general are independent of the chosen base, as long as you do the operations correctly. – MSDG Jul 10 '18 at 13:13
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    "pi" is not a formula. The other ones wouldn't change in any way. – Wojowu Jul 10 '18 at 13:13
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    The numbers $5$ $15$ $25$ $35$ $45$ and $55$ do not belong in your list. – dan post Jul 10 '18 at 13:19
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    Numbers are numbers. They don't change just because you choose to write them using a different base. – MPW Jul 10 '18 at 13:21
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    Perhaps that you might want to know that, in base $5$, $\pi=3,03232214\ldots$ – José Carlos Santos Jul 10 '18 at 13:21
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    Note that the system using the numerals $0$ through $5$ is base six (just like the system using the numerals $0$ through $9$ is base ten, not base nine) – BallBoy Jul 10 '18 at 15:30

3 Answers3

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The representation of $\pi$ will change, but the value of $\pi$ will not change.

None of the formulae change.

gandalf61
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Formulas are independent from the base you use.

Every number will be converted correctly and properly, and thence you would keep using the same "old" formulas as always. What will change will be the involved numbers, not the formulas.

Enrico M.
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Short answer: They wouldn't change at all.

MPW
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