On Fri, Dec 28, 2012 at 12:31 PM, Paul Tanner <email@example.com> wrote: > > This feeble attempt to change the subject won't work. The context here > is denial of mathematical theorems, pure and simple. There is no > debate in the denial of a theorem. >
So may I conclude you're against this strategy of arguing pro and con a mathematical proposition?
Lets remember that the calculus was not originally well received in all corners because it seemed insufficiently justified. Newton's early "proofs" were not always accepted as such, e.g. by Bishop Berkeley, who thought Newton was putting one over on us. Berkeley wasn't regarded as a crackpot by his peers, and a university was named after him.
Likewise Kronecker thought Cantor was nuts (a crackpot) yet today people celebrate parts of Cantor's thinking. Can a person be a genius and a crackpot at the same time?
Wasn't Newton a crackpot where his alchemy was concerned? Or maybe not, just a genius in a different way? Do you have an opinion?
Surely you're not suggesting mathematics should be presented as free from controversy, as that would go against the historical facts.
Anyway, you seem to be changing the subject way from the question at hand.
Am I correct that you see each vertex approaching an ideal of 360 degrees around it (perfect flatness) at a limit?
Would that be a theorem or a definition?
Or might you say "as long as it's not a perfect sphere, but a mathematical structure made of vertexes (V) connected by edges (E) forming a spherical network of windowed openings (F), it's not approaching true sphere-hood and therefore the sphere-at-the-limit concept does not apply." ?
I assume you accept Descartes' Deficit as proved, so clearly each V contributes a finite iotum to the total 720. There's no question of us ever reaching some "ideal" of zero deficit as that would contradict the need for 720 total. 720/n is never zero if n is an actual integer.
Also: V + F == E + 2 (also provable in this case, but not necessarily relevant -- included for review).
And: If N = V - 2 then N:F:E == 1:2:3 and V = 10 * f * f + 2 where f = frequency (intervals between pentagons).