e and pi are based on what we think is randomness

[Kedas]

There is an article in New Scientist about it but no article on there site.

 

found some other link about it here:

http://www.math.uwaterloo.ca/navigation/ideas/grains/pi.shtml

 

It's not news but I didn't hear that before but it's sure interesting.

[Woxor]

You could probably figure out a way to estimate any number this way -- I don't think pi or e or even the irrationals are unique in this respect.

 

Also, Buffon's needle requires something like [math]10^{8}[/math] trials to yield a reasonable approximation of pi to 4 decimal places -- not very practical.

[bloodhound]

there another way as well. instead of using parallel lines like in buffon, use two sets of parrallel line perpendicualr to each other

[Kedas]

You could probably figure out a way to estimate any number this way -- I don't think pi or e or even the irrationals are unique in this respect.

Yeah, I wonder about that also maybe it's just a statistical trick to come to that number.

Like calculate the average then group those above seperate of those below if you devide the amount of numbers you have above with the number of numbers below average then you get the magical number '1' out of this random numbers

 

Also, Buffon's needle requires something like [math]10^{8}[/math'] trials to yield a reasonable approximation of pi to 4 decimal places -- not very practical.

If it's practical or not isn't important the fact that you can do it is much more interesting (assuming you can't do it for every number).

[Woxor]

Yeah' date=' I wonder about that also maybe it's just a statistical trick to come to that number.

Like calculate the average then group those above seperate of those below if you devide the amount of numbers you have above with the number of numbers below average then you get the magical number '1' out of this random numbers [/quote']For example: you can approximate 3.5 by rolling a six-sided die a bunch of time and averaging the results.

 

In general: the expected value of the variable Y=f(X) (expressed as "E(Y)")can be approximated by simulating a randomized value of X a bunch of times, running it through the function, and taking an average. Since we can simulate your average, linearly-distributed variable (using dice, computers, or creative things like Buffon's needle), and since for any real number R, we can dream up an f such that E(f(X))=R, we can use this method to approximate any real number. I suppose you could also do it with complex numbers, or even something as abstract as surreals, but you would have to know far more about non-standard probability (if that's even a subject) than I.

 

If it's practical or not isn't important the fact that you can do it is much more interesting (assuming you can't do it for every number).

I'll certainly grant that it's interesting, though like I said I do think it's possible to derive some experiment to approximate any given number. It does certainly agitate the old curiosity about why e and pi behave like they do and why they have the particular, seemingly-arbitrary values they have.

[alt_f13]

Pi describes the diameter of the universe in relation to its circumference and e equals the ratio of root level units of space per unit of energy in the universe...dur.

 

Simple advanced nano-atomical phisics, you all should know this by now.

 

And for those of you who didn't know, yes, the universe is a circle. A visibly two dimensional shape whose third dimension is a value held in the fourth real dimension:

 

the groovy dimension. And the meaning of life is what? You guessed it!

 

Disco!!!!!1112

 

there another way as well. instead of using parallel lines like in buffon, use two sets of parrallel line perpendicualr to each other

 

What is this you are talking about?