This is a more open ended thing. I’m trying to cram and finish a presentation in these last couple of days, so I don’t have much time for my own maths. But, looking at this picture, lifted from Mathworld,
What are some questions that immediately spring to mind? One in particular springs out at me.
Increasingly, I find that being able to ask interesting questions is as important a skill, if not more so, than being able to answer them.
So, interesting math questions – go.
Does the radius approach a limit? Or define the radius as a function of the number of sides n, (starting at 3), I guess would be my questions
Comment by Foxfan — July 12, 2009 @ 6:03 pm
Nah actually I found a formula for the radius and it isn’t that interesting.
More interestingly, I was trying to find a function to fit to the line that goes through the first verticies of each polygon you encounter going counterclockwise from 3oclock. I can’t get it into form without n’s.
Comment by Foxfan — July 15, 2009 @ 3:33 am
Hmm, questions that immediately spring to mind:
-If the radius approach a limit, what is it in terms of the innermost circle’s radius? (One could just assume it to be 1, of course.)
-How fast is the radius converging to a limit? (I think the speed of convergence would be similar to that of the sequence of polygons Archimedes used to approximate Pi.)
-If the figure were in 3D, what would change?
Hmm…well, I suppose my questions are not particularly interesting. XD
Comment by Alex — September 11, 2009 @ 2:11 am