no magic here

We never got taught that, and I'm year 11

To anyone that may not know aht that is it is taking 2 side of a 90 degree triangle and putting them in the equation a2+b2=c2

The "repeat until infinity bit" is where the problem is, since it'll always be an overestimate of the circumference. A similar example can be seen when you use trapeziums to try and find the area underneath a curve between two points. I tried to make a diagram here, and it's really shitty, but anyway, we shall advance.

There'll always be a space between the "Square"'s perimeter when the corners are "removed" and the circle. When the space is big at the start it's easy to see, but when the spaces get smaller, the area between them is more spread out, so it's harder to see due to the diagram you have there..

I guess that is the reason, I guess an infinite number of little nitches would have a large perimeter.

Hm, my head hurts. Will try to work out.

Meanwhile please have this proof that pi=3.14. You may have seen it before but OH WELL!