New sections on nspheres, sum of a polygon's internal angles

An enlightening discussion about pi and tau.

New sections on nspheres, sum of a polygon's internal angles

by josephlindenberg » Mon Apr 23, 2012 4:25 pm

Mike, I recently added two new sections to my tau website on topics that were addressed in the Pi Manifesto. When you have a moment, would you take a look and tell me what you think? (Anyone else still here, feel free to chime in too.) Thanks.

http://sites.google.com/site/taubeforeitwascool
"The sum of the internal angles of a polygon - A rebuttal"
"A different pair of formulas for every dimension. Their common link?"
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
josephlindenberg
Elementary School
Elementary School
 
Posts: 18
Joined: Wed Jul 06, 2011 2:34 am

Re: New sections on nspheres, sum of a polygon's internal an

by SpikedMath » Wed Apr 25, 2012 5:16 pm

Very nice discussion on "uninternal angles". I'm not sure if that's the best name for them but can't think of anything better -- too bad external angles is already taken! However, since we're changing the circle constant we might as well change the definition of 'external angle' as well! 8-)

The next section is nicely written too. The diagram (Nspheres.png) was confusing at first until I realized the red things were arrows (which it does say after the diagram). Let me think about it for a bit and see if I can come up with a clever rebuttal, hmmm....
Math - It's in you to give.
User avatar
SpikedMath
Site Admin
Site Admin
 
Posts: 133
Joined: Mon Feb 07, 2011 1:31 am
Location: Canada

Re: New sections on nspheres, sum of a polygon's internal an

by xander » Wed Apr 25, 2012 6:36 pm

How about "outside angle"? Or, if we want to be really clever, "outernal angle"?

xander
User avatar
xander
University
University
 
Posts: 154
Joined: Fri Feb 11, 2011 12:14 am
Location: Sparks, NV, USA

Re: New sections on nspheres, sum of a polygon's internal an

by josephlindenberg » Wed Apr 25, 2012 8:04 pm

Since it has done without one this long, it would appear mathematics doesn't really need a name for the "uninternal angles". I just needed something to call them for purposes of this discussion, and I intentionally chose an awkward name. I considered using "outside angles", but I didn't want people getting too comfortable with the name and then absent-mindedly swapping in synonyms like "external". You know how our brains can work -- outside, external, same thing. That's also partly the reason I color-coded the names.
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
josephlindenberg
Elementary School
Elementary School
 
Posts: 18
Joined: Wed Jul 06, 2011 2:34 am

Re: New sections on nspheres, sum of a polygon's internal an

by bmonk » Thu Apr 26, 2012 11:43 am

It's nice, though. And fits my thoughts on the subject. The formula for the angles of a polygon is not real obvious or simple to my mind, but going by the uninternal angles makes it very simple: the sum is 720° or τ, no matter how many angles are involved.
bmonk
University
University
 
Posts: 140
Joined: Thu Feb 10, 2011 4:03 pm

Re: New sections on nspheres, sum of a polygon's internal an

by josephlindenberg » Sun May 13, 2012 10:02 pm

Thanks for pointing out the problem with me not explaining the diagram, Mike. I've rewritten that n-spheres section, and I added a better introduction of the diagram.
PI is the SEMICIRCLE constant, not the circle constant . . . http://sites.google.com/site/taubeforeitwascool
josephlindenberg
Elementary School
Elementary School
 
Posts: 18
Joined: Wed Jul 06, 2011 2:34 am

Re: New sections on nspheres, sum of a polygon's internal an

by rdococ » Mon Sep 16, 2013 11:09 am

bmonk wrote:It's nice, though. And fits my thoughts on the subject. The formula for the angles of a polygon is not real obvious or simple to my mind, but going by the uninternal angles makes it very simple: the sum is 720° or τ, no matter how many angles are involved.

You forgot already that [tex]\tau[/tex] = 360 degrees, because [tex]\pi[/tex] is wrong.
rdococ
Elementary School
Elementary School
 
Posts: 13
Joined: Tue Sep 10, 2013 11:23 am

Re: New sections on nspheres, sum of a polygon's internal an

by bmonk » Sat Sep 28, 2013 3:52 pm

rdococ wrote:
bmonk wrote:It's nice, though. And fits my thoughts on the subject. The formula for the angles of a polygon is not real obvious or simple to my mind, but going by the uninternal angles makes it very simple: the sum is 720° or τ, no matter how many angles are involved.

You forgot already that [tex]\tau[/tex] = 360 degrees, because [tex]\pi[/tex] is wrong.

True. But the point is that the sum of any polygon's external angles is 2[tex]\tau[/tex]. If you want the sum of the internal angles, then you need to calculate a bit more.
bmonk
University
University
 
Posts: 140
Joined: Thu Feb 10, 2011 4:03 pm

Re: New sections on nspheres, sum of a polygon's internal an

by 1=0 » Sun Mar 19, 2017 7:42 pm

bmonk wrote:
rdococ wrote:
bmonk wrote:It's nice, though. And fits my thoughts on the subject. The formula for the angles of a polygon is not real obvious or simple to my mind, but going by the uninternal angles makes it very simple: the sum is 720° or τ, no matter how many angles are involved.

You forgot already that [tex]\tau[/tex] = 360 degrees, because [tex]\pi[/tex] is wrong.

True. But the point is that the sum of any polygon's external angles is 2[tex]\tau[/tex]. If you want the sum of the internal angles, then you need to calculate a bit more.


The sum of any polygon's external angles is just tau, not 2τ, and just 360°, not 720°. Are you thinking of something else?
τ>π
1=0
Mathlete
Mathlete
 
Posts: 41
Joined: Sun Mar 19, 2017 11:01 am


Return to The Pi Manifesto



Who is online

Users browsing this forum: No registered users and 1 guest

cron
Fatal: Not able to open ./cache/data_global.php