4 ms·
It's because the tangents to Archimedes' polygons also approach the tangents to the circle. (This is the "velocity vector" convergence condition mentioned by c
by caf 16y ago
It's because the tangents to Archimedes' polygons also approach the tangents to the circle.
(This is the "velocity vector" convergence condition mentioned by cousin_it above).
- jules 16y agoThat doesn't explain why. Why is it that if tangents approach the circle (whatever that means precisely) that the length of the approximation approaches the length of the circle?
- caf 16y agoLoosely speaking, the total path length is defined as the sum of a bunch of infintesimal segments that have both position and direction. For the sum (integral) of those infintesimals to approach the sum of the similar infintisemals around the actual circle, those of the approximation path have to approach those of the circle in the limit, and of course this means in both position and direction.