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 <bob@rsccore.com> wrote:

>

> On Dec 27, 2012, at 6:02 PM, kirby urner <kirby.urner@gmail.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.

Kirby