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What implications would this have for practical sciences?

All thoughts appreciated, ty.

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- #1

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What implications would this have for practical sciences?

All thoughts appreciated, ty.

- #2

chroot

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It would break a very large amount of the mathematical machinery that we have created to date.

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Pi is proven to be irrational, so no danger there.

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- #4

StatusX

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This would have less of an effect on macroscopic physics then quantum mechanics, and QM already has very little effect.

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Who proved Pi to be irrational and could a math novice such as I understand such a proof?

Also, why do mathematician's bother to further refine Pi's value to millions of decimel places, are there formulas that scientists use that make more accurate predictions based on futher refinements on Pi? Perhaps, we can more accurately send a shuttle into orbit or something like this, or is this off base.

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One interesting thing you get from it is to see up to what extent [itex]\pi[/itex] is random (it is assumed to be random but not proven).Also, why do mathematician's bother to further refine Pi's value to millions of decimel places, are there formulas that scientists use that make more accurate predictions based on futher refinements on Pi?

See for instance http://www.mathpages.com/home/kmath519.htm" [Broken] about this but then for e.

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No, there is no particular use for calculating [itex]\pi[/itex] to many decimal places, at least with regard to any practical problem. My computer can calculate [itex]\pi[/itex] to 100,000 digits in a second, and that is with 77 Firefox windows, two Maple windows, music playing, and a number of other programs running (for some reason I've never liked tabs much )! If I required it, I could have 10,000,000 digits in half an hour. Even at the 1,000 digit level there would be no practical calculation that wouldn't include other sources of uncertainty much, much larger.

I'm sure there are many proofs of pi's irrationality online. Just google "proof that pi is irrational," or some such.

I'm sure there are many proofs of pi's irrationality online. Just google "proof that pi is irrational," or some such.

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Here's a proof, and in the first sentence it says who proved it first. You can follow it if you know calculus. There's not really anything to understand though. It seems they arrived at a useful inequality more or less by luck.

- #10

HallsofIvy

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That's not true. [itex]\pi[/itex] is a specific number that is definitely irrational. What you should say is that the could exist a portion of space in which the ratio of circumference to diamer of a circle is a rational number rather than [itex]\pi[/itex]- but that has no effect on the number [itex]\pi[/itex].

This would have less of an effect on macroscopic physics then quantum mechanics, and QM already has very little effect.

- #11

JasonRox

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I don't know much about this. But even if we were in a different space where the ratio was rational, we probably have to use Pi itself to even solve the ratio in the first place. :uhh:That's not true. [itex]\pi[/itex] is a specific number that is definitely irrational. What you should say is that the could exist a portion of space in which the ratio of circumference to diamer of a circle is a rational number rather than [itex]\pi[/itex]- but that has no effect on the number [itex]\pi[/itex].

- #12

HallsofIvy

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No, I see no reason for that. Certainly we can imagine a world where ratio of circumference to diameter of some circles is 3. No need to introduce pi at all.

(I said**some** circles because while in Euclidean geometry that ratio is the same for all circles, pi, in any non-Euclidean geometry, it varies with the size of the circle.)

(I said

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- #13

Gib Z

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If we were in a different space where the ratio of rational, we would make bigger problems for ourselves by using pi because since pi is irrational, the constant by which you multiply pi to get this rational value must also be irrational and an expression involving pi. I seemed to be quite confusing there...

- #14

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Because of the following remark:

I thought that OP was interested in the usualWhat implications would this have for practical sciences?

I realize this is the math forum, but the math interpretation of the OP's question is so nonsensical I treated it as a misplaced physics question.

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- #16

HallsofIvy

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What do you mean by a "quadratic number system"? And exactly what are you asking?

- #17

arildno

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In any other integer base than 10, pi is still irrational.

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n/m. scratch that.

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Just a thought, nothing more.

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If pi is normal, then yes, otherwise that's not at all guaranteed. 1.01001000100001... is irrational, but the number combination "2" never appears at all (this is a decimal representation!).Since Pi is irrational, would it be logical to think that the string of digits go through every possible number of combinations?

All evidence suggests that pi is normal, though no one's been able to prove it yet...

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- #22

HallsofIvy

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If you mean representing it as a