How many sides does a Paragon have?

[Paragon]

O8)

:evilgrin:

[Dookus]

1. hrmm.....

it depends. Are you multi-dimensional?

[Paragon]

2. Like a bad Star Trek episode, baby.

:silly:

[oxymoron]

3. With or without

psychotropic drugs?

[oxymoron]

5. whoa

was that a waste of my 700th post or what?

[htuttle]

4. I'd guess...

... (the square root of 2) number of sides. It has to be some irrational number....

[NoPasaran]

6. One less

Than a paradox

[Robb]

7. You get three sides

with a Paragon. I usually go with coleslaw, mashed potatoes, and rolls. :)

[Paragon]

9. Dingbat.

:silly:

[Orangepeel]

8. I say two. It used to have four, but one pair is a gone.

[patriotvoice]

10. I wouldn't exactly label this "rigorous," but....

"For a want of a better term, the word paragon was used to designate a polygon whose opposite sides are parallel and equal. Following Kasner and Newman's construction of parahexagon, paragon is obtained by averaging N successive vertices of an arbitrary 2N-gon. Allowing for vertex repetition, we may as well average 3N, 5N, 7N, etc. vertices at a time. It's almost as obvious that averaging over any other number of successive vertices will produce a paragon. But what if we iterate the process? Choose K and form 2N averages of K successive vertices of a polygon. If need be, repeat the process. Does there exist a K, other than N, 3N, 5N, ..., such that after a number of iterations the resulting polygon is paragon?"

http://www.cut-the-knot.org/Curriculum/Geometry/Barygon.shtml

[arwalden]

11. One More Than An Optigon.