# Pi - too many digits

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 1257812.  Wed Oct 25, 2017 12:02 pm Edited to: on second that, let's not go down another tangent.Last edited by dstarfire on Wed Oct 25, 2017 12:07 pm; edited 1 time in total

1257813.  Wed Oct 25, 2017 12:02 pm

 Alexander Howard wrote: There's an infamous story about an American "mathematician", Edwin J. Goodwin, who devised a system where π would equal 4. How mad it got after that I do not know, nor do you really need to know any more.

Not true. He was trying to copyright his method for "squaring the circle", which had already been proved impossible, and tried to get it passed into Indiana state law. His method assumed that pi had the value 3.2:

http://mentalfloss.com/article/30214/new-math-time-indiana-tried-change-pi-32

Last edited by GuyBarry on Wed Oct 25, 2017 12:16 pm; edited 1 time in total

1257814.  Wed Oct 25, 2017 12:14 pm

dstarfire wrote:
 GuyBarry wrote: The universe doesn't have a circumference, since it doesn't have a boundary. I think you mean the circumference of the observable universe. Still a lot less than 22 trillion though :-)

How do we know there isn't a boundary? Has somebody managed to observe, even indirectly, that area? (Unlikely since it's getting father away from us at superluminal speeds.)

Well no, because it's not observable from the Earth. Any part of the universe that's further away than the distance that light could have travelled to the Earth since the Big Bang is, by the laws of physics, unobservable from the Earth. That doesn't mean that it doesn't exist.

 Quote: Also, you don't need a barrier to have an edge. 1. According to the big bang theory, all matter in the universe occupied a single point at the beginning of time. 2. The universe is expanding at a given rate. 3. The universe has a definite age. 4. Ergo there exists a common point beyond which it's impossible for matter to have travelled naturally.

And you think that the point it all expanded from is the Earth?

Do you seriously believe that the universe is a perfect sphere with its centre at the Earth? That would take the anthropocentric assumption to new limits.

 Quote: Finally: What, are you chairman of the pedantic society?

Well, you made the original point. On a forum like this, you need to be able to back up your assertions.

1257883.  Wed Oct 25, 2017 8:51 pm

D*mnit, didn't delete fast enough. Oh well, if we're going to go down this tangent, might as well do it properly.
 GuyBarry wrote: And you think that the point it all expanded from is the Earth? Do you seriously believe that the universe is a perfect sphere with its centre at the Earth?

I don't recall saying the earth is the center, and I certainly didn't mean to imply that. I know that there is NO CENTER, and that everywhere is the center. Expanding space is somewhat counter-intuitive like that.

Quote:
 Quote: Finally: What, are you chairman of the pedantic society?

Well, you made the original point. On a forum like this, you need to be able to back up your assertions.

It's the start of a joke from the "Groovy" episode. The punchline is "vice-chairman, actually".

1259757.  Sun Nov 05, 2017 4:16 pm

Alfred E Neuman wrote:
 GuyBarry wrote: Yes, but it's not much use if you're trying to calculate quickly in your head!

True. But there’s not that much of that being done these days.

I still do occasionally (using 3.14). Also sometimes on paper (using anything up to 3.14159 depending on how pretentious I feel). I don't carry a calculator, so sometimes you need to do a quick measure. Also it keep the brain from atrophying.

1259758.  Sun Nov 05, 2017 4:18 pm

 Paul-R wrote: Also it keep the brain from atrophying.

You don't say.

1259763.  Sun Nov 05, 2017 4:38 pm

Alfred E Neuman wrote:
 Paul-R wrote: Also it keep the brain from atrophying.

You don't say.

Think what it would be like if I didn't do this!

 1261287.  Sun Nov 12, 2017 4:43 pm For a working paper approximation of Pi we (the students on the Mathematics degree course at the University of Sheffield ca. 1993 / 1994) were given the ratio 355/113. This handy approximation is correct to 6 decimal places.

 1261344.  Mon Nov 13, 2017 6:39 am Indeed - it's known as Milü, and is a remarkably close approximation for a fraction with such a small denominator. To get a closer rational approximation you need five digits in the denominator - 52163/16604, which is hardly closer than 355/113. To get seven decimal places, you need 86953/27678. There's an interesting article here about its unusualness.

 1261366.  Mon Nov 13, 2017 9:51 am Footnote: the renowned Indian mathematician Srinivasa Ramanujan discovered that the fourth root of 2143/22 approximates pi to an astonishing eight decimal places (3.14159265258...). Not a lot of practical use unfortunately!

1261549.  Tue Nov 14, 2017 1:59 pm

 GuyBarry wrote: Indeed - it's known as Milü, and is a remarkably close approximation for a fraction with such a small denominator. To get a closer rational approximation you need five digits in the denominator - 52163/16604, which is hardly closer than 355/113. To get seven decimal places, you need 86953/27678. There's an interesting article here about its unusualness.

Thanks. I'd never heard of Milü (I never got to the end of the Mathematics degree!)
I wonder if there is a similar approximation for e?

 1261557.  Tue Nov 14, 2017 2:38 pm 2721/1001 gives you six decimal places. 271801/99990 gives you nine - it evaluates to the repeating decimal 2.7182818281828..., and by sheer fluke the decimal expansion of e repeats four digits in the first nine places (2.7182818284590...). I suspect that rational approximations to e aren't studied so much because, unlike pi, e isn't a ratio, but a base for logarithms. Do you know anything about continued fractions? There's something very unusual about the value of pi - its continued fraction representation has a very high term early on, namely [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2...] Whereas the continued fraction representation for e is [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1,...]. This has a clear pattern to it, unlike the one for pi, but it means that no high terms occur early in the expansion.

 1267145.  Sun Dec 17, 2017 3:14 pm bit of a side note from approximations but a few mathematicians, called tauists, think "pi is wrong" (as a concept) and would prefer to use tau, twice pi, as it's a more natural unit that represents the whole 360 degrees of a circle. They've even written a lengthy manifesto and prefer to refer to the 14th March (3/14 in America), agreed on by congress to be Pi Day, as Half Tau Day. However, what they really want is the recognition of the 28th June as Tau Day. Sources: https://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/ https://tauday.com/tau-manifesto

1267152.  Sun Dec 17, 2017 4:10 pm

 spectacles wrote: bit of a side note from approximations but a few mathematicians, called tauists, think "pi is wrong" (as a concept) and would prefer to use tau, twice pi, as it's a more natural unit that represents the whole 360 degrees of a circle.

I don't think I would say that π is "wrong", but I agree that 2π does seem to crop up more often than π in mathematical formulae. About the only common formula where π appears without the factor 2 is the one for the area of a circle (πr^2).

It would probably have been better historically if the ratio of a circle's circumference to its radius had been taken as the fundamental one; but I can't see centuries of mathematical writing being overturned. It's just one of those little inconsistencies we have to put up with.

 1267240.  Mon Dec 18, 2017 9:39 am Numberphile love this shit: https://www.youtube.com/watch?v=83ofi_L6eAo

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