Does Pi terminate or never?

[Towlie]

Here's an irrational number: 1.101001000100001000001...

You and the people who posted after you are arguing that if you rule out certain digits or combinations in your definition of a number then those digits won't appear in the number. That seems petty and trivial. I could just as easily define an irrational number that contains all of the same digits as the square root of two except that whenever the sequence "69" appears it is replaced by "42". That would also be an irrational number that's guaranteed to NOT have every finite number string.

But enough of that. I did, after all, say "probably". I still dispute this statement by Ziggurat:

Also, there's no guarantee that every book, or even any book, is in pi. pi doesn't have to contain every possible finite number string.

 

[Towlie]

We've discussed decimal numbers that go on forever, irrational numbers, and transcendental numbers here. I wonder if Bill Thompson knows the difference.

 

[eeyore1954]

Does Pi terminate or never?
My high school math teacher had a cat named Pi and seeing as that was close to 40 years ago I would bet that Pi did terminate.

 

[readme.txt]

I still dispute this statement by Ziggurat:

<quote by Ziggurat>

As ddt said, it depends on its normality. I suggest you to read this brief article, which explains this well-known math issue : http://www.askamathematician.com/?p=177

It was never proven, therefore it is still a belief. So Ziggurat might not be wrong.

Does Pi terminate or never?
My high school math teacher had a cat named Pi and seeing as that was close to 40 years ago I would bet that Pi did terminate.

 

[readme.txt]

Almost certainly, but of course, "almost certainly" isn't sufficient for a mathematical proof.

http://en.wikipedia.org/wiki/Almost_surely

 

[dasmiller]

http://en.wikipedia.org/wiki/Almost_surely

I had no idea that there was a formal definition! Thanks

 

[orange31]

The point is, Pi never repeats. It does not matter what sort of counting system you use. It never repeats. Ever....
Pi is the length it takes to draw a circle divided by its diameter. The diameter can be an easily determined number 1, 2, 3... but use that straight line as a unit to represent the circumference and you will get a number that can never be accurately 100% represented because you will always be using what amounts to straight line sebments to represent a curve.

No problem that Pi never repeats. But I'm curious why it doesn't repeat. If the reason relates to a difference between measurement on a straight line versus measurement on a curved line, it isn't obvious to me why a repeating decimal is ruled out in that situation. Is there something in calculus that gives insight into that? Long ago a math teacher mentioned that you can actually prove -using calculus- the shortest distance between two points is a straight line.

 

[W.D.Clinger]

No problem that Pi never repeats. But I'm curious why it doesn't repeat. If the reason relates to a difference between measurement on a straight line versus measurement on a curved line, it isn't obvious to me why a repeating decimal is ruled out in that situation. Is there something in calculus that gives insight into that? Long ago a math teacher mentioned that you can actually prove -using calculus- the shortest distance between two points is a straight line.

Any finite sequence of digits in the decimal expansion of pi might be repeated somewhere else in the decimal expansion of pi.

What never happens is that the digits of pi settle down into some finite sequence of digits that repeats infinitely, that same sequence followed immediately by that same sequence, and so on. The reason we know this can't happen is that pi is irrational.

 

[RussDill]

Anybody who's read Contact knows there's a buried message in pi...

That never made sense to me. It would not seem possible given the simple definitions necessary to derive Pi to somehow hide data within it.

Now, a far more interesting plot element would be embedded information in unitless physical constants. The more accurately determined the number, the more data that could be seen.

(ETA: with instructions embedded early on in the sequence for building machines that determine the number with greater accuracy)

 

[gnome]

That never made sense to me. It would not seem possible given the simple definitions necessary to derive Pi to somehow hide data within it.

I'm not sure why that would be an obstacle to the kind of creator Sagan envisioned. You're looking at data that OUGHT to be random and determined by the nature of the very universe itself... but clearly isn't random... a dead giveaway isn't it? It proves you exist and so therefore you don't.

Oh dear, I hadn't thought of that *puff of logic*.

 

[sol invictus]

The fact that people will debate and argue mathematics is proof that we are not an intelligent species. That is what I am getting from this discussion thread.

That makes no sense whatsoever. If anything, it is proof that we are an intelligent species.

That said, who's arguing about anything?

 

[Perpetual Student]

No problem that Pi never repeats. But I'm curious why it doesn't repeat. If the reason relates to a difference between measurement on a straight line versus measurement on a curved line, it isn't obvious to me why a repeating decimal is ruled out in that situation. Is there something in calculus that gives insight into that? Long ago a math teacher mentioned that you can actually prove -using calculus- the shortest distance between two points is a straight line.

This might help: LINK

and (regarding the shortest distance proof): LINK

 

[Soapy Sam]

Given the curvature of spacetime is scarcely zero this close to a star, is it actually true that C/d=pi anyway? Or is this just an approximation?

 

[Audible Click]

I laughed at that. Then I read the caption.

I laughed at it and ignored the caption.

 

[drkitten]

But enough of that. I did, after all, say "probably". I still dispute this statement by Ziggurat:

You shouldn't. As has been already pointed out, Ziggurat's statement is simply that pi has not been proven normal (to base 10, technically), which is true.

 

[Soapy Sam]

What does "normal" mean in that post drk?
This is not a philosophical query, merely one about definition.

 

[JoeyDonuts]

Put it in Pascal's Triangle!

See if it does something!

 

[ddt]

What does "normal" mean in that post drk?
This is not a philosophical query, merely one about definition.

A "normal number" is a number in whose decimal expansion the digits are uniformly distributed (i.e., they all occur with equal probability), as well as all series of two digits, of three digits, etc.; and not only in decimal expansion, but in expansion in an arbitrary (integer) base.

Nearly all numbers are normal.

 

[Soapy Sam]

Ta.

 

[Modified]

Pi is the length it takes to draw a circle divided by its diameter. The diameter can be an easily determined number 1, 2, 3... but use that straight line as a unit to represent the circumference and you will get a number that can never be accurately 100% represented because you will always be using what amounts to straight line sebments to represent a curve.

That is not an explanation, it is some sort of (incorrect) intuition. Any number of closed curves have integer relationships between circumference and some property represented by a straight distance.