Originally Posted by

**becko** I think that breaking the square into smaller squares, each of which contains its own circle, will lead you astray, as it did me. If each square contains its circle and doesnt intersect other circles, then the ratio of area covered to the area of the square remains fixed, no matter what size you make the small squares.

We need a different strategy. A circle must be allowed to penetrate into the squares that circumscribe neighboring circles.

By the way, I think I saw somewhere that the circles of someone (name of important person here) do this. I just can't remember where I saw this, and what was the name of the mathematician.

So you studied with Pugh. Can you share something about him? Was he a good teacher in person? I think the book is pretty good.