I posted this thread here rather than the university thread because of its apparent simplicity. I just can't seem to figure it out what's wrong. too much summer slacking I suppose.

Start with a circle of diameter 1 inscribed in a square of side length 1

Remove corner squares such that the perimeter of the outside polygon doesn't change and doesn't include the area inside the circle.

Repeat the above process infinitely for each new corner generated by this process.

--

The perimeter of the polygon is always 4, but the limit of the perimeter as the number of steps approaches infinity is

. As 4 =

is absurd, what is wrong with this reasoning?