The numerical value for pi

[MyNameIsVu]

Obviously, in theory, the "fastest" in term of practicality is 3.000.. +.100...+.0400...+..., but I don't know as of yet such an alogthrim (excuse my spelling.) What are some of the fast and simple alogthrim for pi. I know two ways, one of them employ calculus to deduce a series approximation but the other is just straight forward geometry and its algebra but eventually uses the concept of limit:

It is suffices to calculate an arc of the circle at a "da." That is, at 1/4 partition multiply by 4 and so forward. Using the unit circle as the fix base, a chore is drawen in the 1st quad. Its bisect is automatically the line that perpendicular to it and y-intercept at (0, 0), thus all info are irrevalent with the exception of slopes. Notate them as (m0, m1, m2, ...). With this sequence of slopes m(n) we can find the length from (1, 0) to point of intersect with the fix circle call it L(n), we can calculate pi/6, via L(n) multiple n as n approach infinity. This, together with the extra control of starting point allow for perhaps extra ease of computation say start at sqr(3/2).

Please list some other method/s here (please note I am not asking for formula)?

Thanks.

[mathman]

Try

http://en.wikipedia.org/wiki/Numerical_ ... nt_formula

[CRGreathouse]

Moved to Applied math (where numerical analysis topics reside).

Generally, the Machin-like formulae are both fast and easy to use. Also worth looking at is the "BBP" spigot algorithm (scare quotes because the third author disputes that the first two authors really had anything to do with it).

[MyNameIsVu]

Much thanks, with the exception to other, what is shown in this post is a bit similar to Lui (unlike the technique/s though), but not sure it is correct as I do not have a calculator:

pi^2/18 = lim(n--->infinity) n^2(1-1/(1+(f^(n)(x))^.5)^(2)), for all x in (0, 1) where f(x) = 2x/(x^2-1) and f^(n) is the n-times composition of f with itself. It should be suitable for computational alogrithms via programming, however an undertaking of it further study is possible through the use of, I just call it "c-derivative where c is in (0, 1)." Note, this equation pointed out more the different between the function symbol and the variable symbol.

Edit: it would seem I made I mistake, it is intended only to work for x = sqrt(3). The general case is just there and it include all positive real with the exception of zero. But the left-hand-side change with each x.

[MyNameIsVu]

And thus we are at a juncture where it make sense to ask can it be possible to graph a linear function in polar coordinate and/or it is plausible to graph a polar function in rectangular coordinate? Certainly, with a fast computing machine that utilized the above mentioned algorithm can be use to dimiss such inquiry or encourage it and it is fruitful in making it accissible to dynamical "random" memory searching scheme, or whatever one chose to call it if it successful