Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: neilep on 24/08/2008 18:12:12
-
Dearest Piologists and eaters of all things pastry lined !
see this Pi ?
[ Invalid Attachment ]
Nice eh ?...being delivered Tuesday !
As a sheep the nature of Pi taunts me every day and night !!
We can calculate Pi to a trillion decimal places !...I know this because I have counted them !.....but why ? Why calculate Pi to a trillion places when apparently only 40 decimal places is enough to calculate the circumference of the visible Universe ?
Whilst I await your answers, I think I'll count them again..I think i missed a '3' somewhere around 425 billion !
Thank Ewe
Hugs the Klevur peeps
Shmishes them too !
Neil
Pi Asker and Pie Eater
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
-
I think the object is to test out algorithms for computing such numbers and to demonstrate computer power
-
I think the object is to test out algorithms for computing such numbers and to demonstrate computer power
Thank Ewe syhprum
So, it's really just a mater of ' because we can '...but also as a tool to demonstrate efficiency....
.......I know this might be a silly question but how do we know if Pi to a trillion decimal places is calculated correctly ?
-
One way of 'knowing' is based on various mathematical proofs which can show that pi must lie between two values which can actually be calculated - therefore they can say that they 'know' pi to a certain accuracy i.e. between those limits.
I'm not sure I put that in the most understandable way - sorry.
-
The real answer to the "why?" question is that Mathematicians are all on a different track to the rest of us. Some of them are really loopy. Brilliant but loopy and what would be do without them?
Try to have an ordinary conversation with a good Mathematician about a commonly discussed topic and you can rely on them to take you to places that you would never normally go. Some of my best friends are Mathematicians, I have to say.
-
Possibly...sometime, somewhere, someone will discover that after the umpteenth billion places you have counted up to...it will start to repeat itself. [:0]
-
That would imply that pi is rational (a ratio of two integers). 'They' can prove, quite conclusively, that it isn't. So you won't find a repeat.
-
To see if there would be some pattern.
-
If the sequence is constantly changing then you might expect the occasional, apparently meaningful, embedded pattern. But what would that prove? It's just like monkeys and typewriters.
-
Any and all patterns will occur somewhere in pi. It might take a while to find them.
-
The book, 'The Life of Pi' is much more interesting. The first few chapters are dull but then....wow! it is brilliant.
Sheepy, I think 7 decimal places is enough for anyone but I guess you can't have too much of a good thing.
-
Parraleling the hunt for evermore digits of Pi the hunt for the 45th Mersenne number seems to have succeeded as reported in the Scientific American this when verified will earn a $100,000 prize
-
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:
4 1^2 2^2 3^2 4^2 k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
1+ 3+ 5+ 7+ 9+ 2k+1+
While other methods converge to pi more quickly, this is the easiest-working.
-
Is it even possible to display a trillion digits ?
-
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:
4 1^2 2^2 3^2 4^2 k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
1+ 3+ 5+ 7+ 9+ 2k+1+
While other methods converge to pi more quickly, this is the easiest-working.
How does that method work? I'm no maths wizz, actually I'm mathamatically dyslexic, but its not that uncommon, 436 people out of 34 have it... mwhahahaha
-
Though I too am fascinated by the trillion digits of pi so far calculated, it's more important to know HOW to calculate it. For example, this continued fraction will do nicely:
4 1^2 2^2 3^2 4^2 k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
1+ 3+ 5+ 7+ 9+ 2k+1+
While other methods converge to pi more quickly, this is the easiest-working.
How does that method work? I'm no maths wizz, actually I'm mathamatically dyslexic, but its not that uncommon, 436 people out of 34 have it... mwhahahaha
They've used what is called a Infinite Series.
-
So can somebody demonstrate for me how its done? How does this Infinite Series work? As I said, my maths isn't exactly out of this world... [:I] [:I]
-
So can somebody demonstrate for me how its done? How does this Infinite Series work? As I said, my maths isn't exactly out of this world... [:I] [:I]
well, i only glanced very quickly at the math, but generally speaking, if you want to calculate something large, then it goes through a series.
-
Um... forgive me for saying this Mr. Scientist, but you are still talking in riddles. [:I] [:I]
-
Um... forgive me for saying this Mr. Scientist, but you are still talking in riddles. [:I] [:I]
Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
-
Even better, here is a link
Series (mathematics) - Wikipedia, the free encyclopedia
A series may be ... However, infinite series of nonzero terms can also converge, ... The idea of an infinite series expansion of a function was ...
en.wikipedia.org/wiki/Series_(mathematics) - 73k - Cached
-
Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
I know a little bit of calculus [:I] If you can explain how that Infinite Series works to solve π I would be very greatful [:)]
-
Do you know calculus? Or would you like me to hopefully explain this in some effecient way for you to understand?
I know a little bit of calculus [:I] If you can explain how that Infinite Series works to solve π I would be very greatful [:)]
It will take me about 20 mins then to type it out. Hold on. :)
-
WOW! Must be some complicated stuff [:o], never mind, I can wait... the mystery of pi shall be explained. Umm... pie... [:P] [:P] [:P] [:P]
-
Right, first contemplate what is a string or a sequence of numbers:
1, 1/2, 1/3, 1/4, 1/5
if we dot it at the end like so,
1, 1/2, 1/3, 1/4, 1/5...
It means, ''and so on,'' in this particular pattern. We can now say that the n^th number is a_n, then one can evaluate that a_1 is 1, and a_2 is 1/2, so that implies that a_n=1/n. An infinite series of numbers will look something like this:
∑ = 1 + 1/2 + 1/4 + 1/8 + ...
Where again, the (+ ...) means an infinite continuation of the numerical processes. Since we can't add all of infinite numbers, we can however add the first lot of ''n'' terms like
∑_1 = 1
∑_2 = 1 + 1/2 = 3/2
∑_3 = 1 + 1/2 + 1/4 = 7/4
where ∑ just means the 'sum of.'
Does that help?
-
WOW! Must be some complicated stuff [:o], never mind, I can wait... the mystery of pi shall be explained. Umm... pie... [:P] [:P] [:P] [:P]
It's not really too complicated. It's just i had other things to do to lol
-
Right, first contemplate what is a string or a sequence of numbers:
1, 1/2, 1/3, 1/4, 1/5
if we dot it at the end like so,
1, 1/2, 1/3, 1/4, 1/5...
It means, ''and so on,'' in this particular pattern. We can now say that the n^th number is a_n, then one can evaluate that a_1 is 1, and a_2 is 1/2, so that implies that a_n=1/n. An infinite series of numbers will look something like this:
∑ = 1 + 1/2 + 1/4 + 1/8 + ...
Where again, the (+ ...) means an infinite continuation of the numerical processes. Since we can't add all of infinite numbers, we can however add the first lot of ''n'' terms like
∑_1 = 1
∑_2 = 1 + 1/2 = 3/2
∑_3 = 1 + 1/2 + 1/4 = 7/4
where ∑ just means the 'sum of.'
Does that help?
(And i can't explain it any more simpler, i am afraid) - so don't ask :)
-
Yeah, all of the stuff about the series I totally understand, what I don't get is how the series:
4 1^2 2^2 3^2 4^2 k^2
pi = ---- ----- ----- ------ ----- ... ------- ...
1+ 3+ 5+ 7+ 9+ 2k+1+
adds up to find pi. What is the range of values for 'k' and what is the 1+ 3+ 5+ doing there?
-
I mean, am I not meant to substitute values of 'k' from 1 to infinity into the series? But doing it on my calculator, I've gotten nothing even close to pi...
-
I don't know how that works out.
-
So we are back to square one, can anybody help me and my imcompetent mathematical brain to uncover the mystery of pi? Mainly, how is the serie/formula thing supposed to work?
-
I've just found pi to 1 million digits: http://www.eveandersson.com/pi/digits/1000000 [:o] [:o] [:o] [:o]
-
I don't know why anyone would want to derive pi other than simply stating 7/22.
-
Isn't it 22/7?
-
I've solved the problem. Its a continued fraction, as found in wikipedia:
WEB RESULTSPi - Wikipedia, the free encyclopedia
Article about the mathematical constant, pi, including its history, appearances in formulae, trivia, and more. ... Retrieved from "http://en.wikipedia.org/wiki/Pi" ...
en.wikipedia.org/wiki/Pi - 182k - Cached
So here, the function that the person was using which caused so much confusion was in fact a continued fraction.
-
(Which is a series, not to confuse matters further)
-
Isn't it 22/7?
Yes, sorry, muddled up.
-
Continued fraction? [???] You're forgetting that you are talking to a mathimatical dyslexic. [::)] hmmm... I think I'll leave the solving to the computers, with that formula I would need to imput millions of numbers into my calculator just to get a remotely accurate number... I'll be sitting here for days [xx(] [xx(]
-
Well, remotely accurate being 22/7. Its about as close as a human can get holding a calculator, without pressing the pi button.
-
I must be going nuts?
I actually enjoyed reading that wiki about pie?
Especially rhubarb :)