Troll proof

[noh_mercy]

I came across this so called proof that pi = 4

[IMG]http://www.base5forum.it/upload/1290616506315.jpg[/IMG]

And before you tell me wat I already know, Im gonna tell you wat I already know. And I already know pi is not 4. pi is the ratio of the circumference of a circle to its diameter.

I started this thread to offer a theory as to why its not 4.

My theory is basically as the amount of those right angle cuts approach infinity, I was thinking that the perimeter does change, and at first that sounds illogical, but hold on. I think that If I made infinite cuts around that square, my circumference would become pi. As you can see the pixel 'circle' is made up of only right angle corners, the more cuts that I make, the smaller and smaller the length of the x and y components of each corner become. At infinity, the length of the x and y components of the corner is 0, so you don't have a corner anymore, you have an infinitesimally small dot. Every infinitesimally small dot connects tangentially to the boundary of the real circle perfectly, and because the x and y component lengths are now 0 they cannot add together to give you a perimeter/circumference of 4, because they don't exist anymore, just the infinitesimally small dot. The circle of dots now have a circumference of pi instead of 4.

Why am I thinking this way? well I have herd of another theory, and its that no matter how many cuts you make, you will never ever approach a perfect circle, you will always get a more pixely version. If that was the case, then in calculus I should never be able to find the exact area under a curve using an infinite amount of rectangles, my area would always be almost there because its just a more pixely version of the actual area. However that is false, with an infinite amount of rectangles, I can calculate the exact area under the curve if I set the amount of rectangles to infinity. So why can I not use this for the circle in a square? Its essentially the same thing.

Am I correct in my approach? What do you think?

[highlight](User was banned for this post ("Not a proper debate thread, read the sticky" - Megafan))[/highlight]