3 ms·
... and that's roughly what the article does.
by not2b 5y ago
... and that's roughly what the article does.
- ffibdinfk 5y agoYou're missing the basic mystery, which is "How does this generalize? Why does it work for a square of side 2r, but not a square of side r?"
- not2b 5y agoNo, I am not missing it: you need an r that corresponds in some way to the radius: it should be half of the side length, so if you start from the center and expand, you integrate over r. That's why you need the side to be 2r. Unfortunately hacker news doesn't give me a way to draw you a picture to illustrate it. Picture a growing square that goes from a point to the square that you want the area of.
- ffibdinfk 5y agoReally, the business of Euclidean constructions involving apothems and polygons does not touch what's going on here. It is trivial and doesn't generalize. And there's no reason why a square with apothem r is more natural than a square with side r. See Tong's paper.