Could someone please explain the fauly reasoning in the following?
So say I had a square with side length=1 and had a circle inscribed in the square. Then the perimeter of the square is 4 and and the circumference of the circle is pi. If turn the corner of the square inwards then the perimeter is still 4, if you continuie to do this you could get infinitely close to the circle, so the circumference is 4.
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 ****** , 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..