Is Integrating for pi the Best Method for Calculating Accurate Values of Pi?

[cam875]

I was thinking about how to approximate pi accurately and came up with something and all the calculations i did seem to show that its true and I am wondering if its used often for calculating pi or if there is something better?

radius of this circle equals 1 and therefore calcualting a quarter area of a circle and multiplying by 4 we should get pi.

$$\pi=area$$

$$4(\int_0^1 \sqrt{1-x^2} dx) \approx \pi$$

 

[rochfor1]

That's true, but you have to think about how you're going to approximate the numerical value of that integral. A commonly used approximation for pi can be derived from the Taylor series for arctangent.

 

[cam875]

is the taylor series the fastest method for calculating pi?

 

[rochfor1]

I don't know what the "fastest" method is. Using Taylor's theorem though you could estimate how quickly the series converges. I just wanted to give a method that you could use that didn't involve approximating an integral.

I imagine a little googling could turn up currently used approximations for pi.

 

[MATLABdude]

I'm not a mathematician, however, you may want to take a look at the Wikipedia article for at least a starting point:
http://en.wikipedia.org/wiki/Computing_pi

Or Mathworld at Wolfram:
http://mathworld.wolfram.com/PiFormulas.html

 

[fleem]

And another consideration is whether you want to create digits in succession or you want to converge toward PI. The latter (which is the method you show) cannot calculate more digits than the floating point variables can hold.