23 Jun
2019
23 Jun
'19
8:49 p.m.
In case that wasn’t clear, I was replying to Adam Goucher’s question, saying that I believe that Archimedes said something that in modern language would be that if L is a compact subset of R^2 and K is a convex compact subset of L, then the perimeter of K is bounded above by the perimeter of L, with equality if and only if K = L. That is: Rather than giving a definition of arc length (as we moderns would feel obliged to do), Archimedes gave a characterization of arc length that is just as useful. Jim Propp