On Thu, Dec 27, 2012 at 3:08 PM, Robert Hansen <firstname.lastname@example.org> wrote: > > On Dec 27, 2012, at 6:02 PM, kirby urner <email@example.com> wrote: > > n * (360 - v) = 720 > > > Fine, I was trying to help you see more easily, just substitute that into > what I said... > > The limit(n) * limit(360 - v) as n->infinity and v->360 IS NOT THE SAME AS > limit(n * (360 - v)) as n->infinity and v->360 BECAUSE limit (n) as > n->infinity DOES NOT EXIST. > > Bob Hansen
I don't think your straw man argument helps my students understand how adding the fact of curvature changes the answer.
The limit (360 - v) really could be 0 if perfect flatness is allowed, but when we add the constraint of curvature, then even though everything locally seems to stay the same -- given the epsilon / delta treatment alone (Debater A) -- the added fact of curvature is new information and tells us that as n --> infinity, there's a 720 involved (Debater B).
We didn't have that before. Curvature subtracts fractions of a degree from each vertex. That's knowledge of a global constraint that evades detection under the microscope.