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Pi - too many digits

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dstarfire
1257647.  Tue Oct 24, 2017 9:04 pm Reply with quote

Pi has been calculated to over 1 million digits (probably quite a bit more). However, you only need 32 digits of pi to calculate the circumference of the universe down to a single atom.

I can't remember if this has come up on QI before* but it would be a rather interesting tidbit to toss in to next season.

Shouldn't be too hard for an elf to corroborate this (I'll bet our math specialist has probably even heard this already).

the inevitable followup question of "if that's true, why calculate so many digits of pi?" can be easily explained as curiosity, bragging rights, and it's a good test for computers.

Just don't dig too deeply into the how or you'll crash your brain.

 
monzac
1257655.  Tue Oct 24, 2017 11:34 pm Reply with quote

Someone was interested enough to print it out and make two videos about it, which includes analyses of some of the number patterns and anomalies that occur.

Mile of Pi
A million digits of Pi on one piece of paper (1.05 miles).

The Making of a Mile of Pi
Behind the scenes and more information about the Mile of Pi film.

 
fwk
1257666.  Wed Oct 25, 2017 2:45 am Reply with quote

Calculating pi with pies

 
GuyBarry
1257705.  Wed Oct 25, 2017 5:04 am Reply with quote

dstarfire wrote:
Pi has been calculated to over 1 million digits (probably quite a bit more).


Rather a lot more than that! According to New Scientist, the current record stands at 22,459,157,718,361 digits.

Quote:
However, you only need 32 digits of pi to calculate the circumference of the universe down to a single atom.


The universe doesn't have a circumference, since it doesn't have a boundary. I think you mean the circumference of the observable universe. According to this video you need 39 digits of pi, not 32.

Still a lot less than 22 trillion though :-)

 
crissdee
1257714.  Wed Oct 25, 2017 5:34 am Reply with quote

I think I might have raised this once before, Strawberry will probably find it if I did! I really struggle to think of a scenario where knowing Pi to more than ten places would be neccessary. In truth, just "3" is close enough for most general calculations, "3.141" will deal with 90% of the rest.

 
GuyBarry
1257722.  Wed Oct 25, 2017 5:55 am Reply with quote

"3.142" is a closer approximation than "3.141".

It's really not necessary for most practical purposes to know the decimal expansion of pi at all, since all scientific calculators have a pi button. I suppose if you're trying to estimate a measurement in your head it's useful to know an approximation, but "22/7" is probably the easiest one to use in those circumstances.

 
Alfred E Neuman
1257724.  Wed Oct 25, 2017 6:03 am Reply with quote

3.141 is closer than 22/7.

 
GuyBarry
1257725.  Wed Oct 25, 2017 6:15 am Reply with quote

Yes, but it's not much use if you're trying to calculate quickly in your head!

Now I come to think of it, it's probably easier to think of the approximate value as "3 1/7" rather than "22/7", since 22 isn't always the easiest of numbers to multiply by.

 
Alexander Howard
1257737.  Wed Oct 25, 2017 6:45 am Reply with quote

[quote="GuyBarry"]Yes, but it's not much use if you're trying to calculate quickly in your head![quote]

Oh come on - it's as easy as 3.14159265359.....

 
Alfred E Neuman
1257742.  Wed Oct 25, 2017 6:50 am Reply with quote

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.

 
Alexander Howard
1257743.  Wed Oct 25, 2017 6:57 am Reply with quote

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.

In a Pratchett book, Going Postal (in which the Ankh-Morpork Post Office is being revived) they uncover an Automated Mail Sorter built by B. S. Johnson, and it is explained that the inventor thought pi was too complicated so in this machine "the pie is exactly three". The result opens up unknown dimensions and starts delivering letters that have not actually been written but might have been. I doubt that was the result of Goodwin's "π = 4" concept.

 
GuyBarry
1257810.  Wed Oct 25, 2017 11:55 am Reply with quote

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.


Yes. In which case what I said earlier still stands: "it's really not necessary for most practical purposes to know the decimal expansion of pi at all, since all scientific calculators have a pi button".

 
dstarfire
1257812.  Wed Oct 25, 2017 12:02 pm Reply with quote

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

 
GuyBarry
1257813.  Wed Oct 25, 2017 12:02 pm Reply with quote

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

 
GuyBarry
1257814.  Wed Oct 25, 2017 12:14 pm Reply with quote

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.

 

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