The other day I read an article about an interestin way to obtain number pi. Making a long series of
throws of a needle of length l over a horizontal board with parallel lines made on it (such that the parallels are
evenly separated with a distance between them equal to the length l of the needle), the probability that the
needle will cross a line is 2/PI.
So how do we get that probability from the experiment? we have two ways of doing that:
*We could throw the needle, for example, 100 times. if we call N the number of times the needle crosses a line
and M the total number of times we throw the needle, then the probability that the
needle crosses a line is N/M, and we will have the following estimation of PI: PI = 2*M/N.
* The other way of doing that (a faster way) would be to throw a large number M of needles over the board
and count the number N of needles that lay over horizontal lines. Once again our estimation of PI will be PI = 2*M/N.
DO YOU KNOW ABOUT ANOTHER INTERESTING WAYS OF OBTAINING THE NUMBER
PI ????
Cheers
wow dat was a good method of deriving the value of pi.
well this method shld be tried at the end of the fifth working day in a week
Interesting, but far too much work for me. i prefer an easy way! Like this:
π = ln(-1) ÷ √(-1)
Easy!
That's not a very practical way to experimentally determine the real value of pi. Even when using "experimentally" in a broad meaning (by using computers or math on paper).
In some hours of boredom I've been wondering if it might be possible to determine values of such constants chemically. Totally useless of course (low accuracy) but fun nonetheless! Though I think pi would be very hard, e may well be possible...
| Arnie wrote: |
That's not a very practical way to experimentally determine the real value of pi. Even when using "experimentally" in a broad meaning (by using computers or math on paper).
In some hours of boredom I've been wondering if it might be possible to determine values of such constants chemically. Totally useless of course (low accuracy) but fun nonetheless! Though I think pi would be very hard, e may well be possible... |
You know, if you're actually serious about calculating π experimentally, all you need is a rectangular cup and a standard cylindrical cup that you know the dimensions of and a ruler. Or, alternatively, a standard cylindrical cup that you know the dimensions of, a fluid you know the density of, a scale and a ruler.Another way you could do this is to simulate the experiment on a computer. Or, you could calculate the circumference of a lot of circular objects and divide by the diameter.
I once got really bored in math class and wrote a virus for my T83+ calculator that filled up all the memory with the solution of some repeating random number generation (which was actually a function my friend and I worked on that wasn't really random at all) and then just kept going from there. I had always been fascinated in doing the same experiment with pi (like the Star Trek: TNG where they convince the computer to calculate it) except I could never figure out how to do the calculations. (I didn't want to look it up, that's cheating)
So, I know what I'm doing tomorrow in Algebra II, thanks.
I found this, it's pretty interesting:
http://webonastick.com/pi/ | Indi wrote: |
Interesting, but far too much work for me. i prefer an easy way! Like this:
π = ln(-1) ÷ √(-1)
Easy! |
There is also Machin's formula:
and Leinbintz formula:
(= 1 - 1/3 + 1/5 ...etc)In the past I've taken a CD and measured the circumference and then divided it by the diameter. This was isn't very good, though, because getting a perfect measurement is extremely difficult and the CD probably isn't a perfect circle exactly.
| Afaceinthematrix wrote: |
| In the past I've taken a CD and measured the circumference and then divided it by the diameter. This was isn't very good, though, because getting a perfect measurement is extremely difficult and the CD probably isn't a perfect circle exactly. |
Direct observation is always best.
How accurate is Machin?
The infinite series implies pi is transcendental (beyond calculation by machine). | Bikerman wrote: |
There is also Machin's formula:
|
If you're going to go down that road, why not just 2 × arccos(0)?
| newolder wrote: |
| The infinite series implies pi is transcendental (beyond calculation by machine). |
oh? ^_^ an infinite series implies a transcendental number?
so:
∴ 1 is transcendental.
^_^; | newolder wrote: |
| Afaceinthematrix wrote: | | In the past I've taken a CD and measured the circumference and then divided it by the diameter. This was isn't very good, though, because getting a perfect measurement is extremely difficult and the CD probably isn't a perfect circle exactly. |
Direct observation is always best.
How accurate is Machin? |
Very accurate...there is a proof of the formula here :-
http://milan.milanovic.org/math/english/pi/machin.html
| Quote: |
| The infinite series implies pi is transcendental (beyond calculation by machine). |
True. | Bikerman wrote: |
| newolder wrote: | | Afaceinthematrix wrote: | | In the past I've taken a CD and measured the circumference and then divided it by the diameter. This was isn't very good, though, because getting a perfect measurement is extremely difficult and the CD probably isn't a perfect circle exactly. |
Direct observation is always best.
How accurate is Machin? |
Very accurate...there is a proof of the formula here :-
http://milan.milanovic.org/math/english/pi/machin.html
| Quote: | | The infinite series implies pi is transcendental (beyond calculation by machine). |
True. |
More play-time?
My own estimate from tools to hand has pi a bit bigger than 3.
The other tools hereabouts allow me to renormalise this group of investigation to whatsover i choose. 
Henceforward, 1/(8piG)^1/2 = 1 and the units follow... (Neater equations too.) 
I always remember it as 22/7. It easier than throwing needles around 
I think that nisibdv was not proposing formulas or easy (or fast) ways to find PI, but funny and experimental ways of doing it.
For example, throwing grains of rice on a square board with a circle inscribed in it and counting the number of times the grains land on the circle and then divide it by the number of times we throw a grain.
ahhh.. the old dusty ball trick. 
Actually I have a friend which knows over one hundred of digits in pi..
Earlier I knew about eighty but they have begun to fall away
Talk about meaningful spent freetime Here's a page I came across which uses simple geometry to calculate pi - it has a nice little app which demonstrates the method:
http://home.hccnet.nl/david.dirkse/math/pi_calc.html | nisibdv wrote: |
The other day I read an article about an interestin way to obtain number pi. Making a long series of
throws of a needle of length l over a horizontal board with parallel lines made on it (such that the parallels are
evenly separated with a distance between them equal to the length l of the needle), the probability that the
needle will cross a line is 2/PI.
So how do we get that probability from the experiment? we have two ways of doing that:
*We could throw the needle, for example, 100 times. if we call N the number of times the needle crosses a line
and M the total number of times we throw the needle, then the probability that the
needle crosses a line is N/M, and we will have the following estimation of PI: PI = 2*M/N.
* The other way of doing that (a faster way) would be to throw a large number M of needles over the board
and count the number N of needles that lay over horizontal lines. Once again our estimation of PI will be PI = 2*M/N.
DO YOU KNOW ABOUT ANOTHER INTERESTING WAYS OF OBTAINING THE NUMBER
PI ????
Cheers |
Well there are a lot of mathematical ways of divining it I find pretty cool. I read somewhere you can do the same thing with frozen hotdogs which is hilariousMy favorite method is Archimede's method... my math teacher and I did it out the other day. It's pure genius.
http://www.gusmorino.com/pag3/pi/archimedes/index.html
And here's a page on calculables too:: http://www.ilemaths.net/encyclopedie/Nombre_r%C3%A9el_calculable.html
(in French but the 'gist' is easy enough to follow.)
It doesn't 'do' the calculation tho' this image does help.
Take any equation where is the pi number, do a little thinking about what equation describes and if you are smart I bet you get thousands of possibilities how to get pi number.
| Jakob [JaWGames] wrote: |
Actually I have a friend which knows over one hundred of digits in pi..
Earlier I knew about eighty but they have begun to fall away
Talk about meaningful spent freetime |
I can remember about 45 digits... That's an error of 1 in 10^45. Not bad.
Calculating pi is still fun to do... wonder if there's hidden information deep inside the digits (like in the book Contact by Carl Sagan)?Ohh, I am also find any difficulty when calculating the pi number using pi = 4*(1 - 1/3 + 1/5 - 1/7 + 1/9 ...) or pi =4*sum ((-1)^k/(2k+1)) form k=0..infinity, because the infinite series is too slowly to converg as explained at so many reference books. I am inspired to Denaya Lesa's way (she is my daughter, please search her road map via google) in remembering 9 digits of pi number like she remembers her handphone number 3-1415-9265. Further, I try to create 9 digits of the pi number by involving square root and number 1.23456789.
OMG I find that pi=1.23456789*sqrt(6.47544755)=3.14159265...and I said on my post at http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=34&start=30 that 6.[47]54[47]55 as a nice numbers, how about you all? After visiting to this link
http://eqworld.ipmnet.ru/forum/viewtopic.php?f=3&t=148
I met a post about the new pi exact formula, maybe useful for you.
i've been meaning to share these for a long time, but never got around to finishing them.
This is an English version of that image, expanded somewhat. It requires a modern browser (like Firefox 3) to be viewed properly.
i also made versions in other languages:
i may add other languages... the only problem is that most other languages i know don't have anywhere near the extensive Wikipedias that these four do. If you want to add a translation, just PM me the translations for these strings:
- First-order definable (set theory)
- Computable number
- Algebraic number
- Rational number
- Algorithmically random sequence
- Incompressible sequence
And links to Wikipedia pages in that language for the following:
Hi all, now Rohedi informs you that at this link
http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=157.
I've been posting the exact formula for Pi number in Phi golden ratio expression. Would you like to know the nice formula? Please visit to the link.Thx.
