hmm i have a new found respect for you.

heh, then maybe you will enjoy this:

well anyway there are methods to approximate the solution to that integral, and by doing an approximation you get a decimal version of pi. There are ways to extend this approximation to as many digits as you want (but each digit requires about 3 additional calculations, see below) so you can get as many decimals as you want, so long as you are willing to invest the time to do the required number of calculations. It is really a very simple operation that you just do a bunch of times (a much better way is to have a computer crunch out these calculations to get as many digits as you want).

here is one way you could do it:

the function y = 4*sqrt{1-x^2) looks like this:


The area of the green shape is equal to pi (on this you will just have to take my word without calculus).

So to get some digits for pi we just need to calculate that area, but its a curve so we can't do it (not without calculus anyway), so lets use old school methods:



Now we do know how to calculate the area of that triangle, but you can see the area of that triangle is not a very good estimate of the area of the whole thing, look at all that extra red stuff we are missing... So lets do this:



Now we have to calculate the area of that trapezoid and that triangle, both of which we can do, and if you look, our estimate has already gotten much better, there is much less red! Anyway you can just keep adding more and more trapezoids and the "extra red section" will get smaller and smaller (and the trapezoids will get narrower and narrower). So you just need to use enough trapezoids to make as good an estimate as you want, use millions if you want (using a computer of course).