Date: Dec 27, 2012 6:24 PM
Author: kirby urner
Subject: Re: A Point on Understanding

On Thu, Dec 27, 2012 at 3:08 PM, Robert Hansen <> wrote:
> On Dec 27, 2012, at 6:02 PM, kirby urner <> 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.