ffibdinfk

4 ms·

1. 1.▲
   by ffibdinfk 5y ago

   Really, 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
2. 2.▲
   by ffibdinfk 5y ago

   You'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?"
3. 3.▲
   by ffibdinfk 5y ago

   The author wants feedback. Well, the article by Tong which is mentioned here https://math.stackexchange.com/a/2092943/124777 gives a deep and surprising reason for the relationship between surface area and volume.