Counting n-gons

[Jonathan Post]

Dr. George Hockney (ex-Fermilab, now JPL) responded to my suggestion that
the representative of each equivalence class of deformed polygons with the
same edge-sequences be that with largest area that: (1)  this might not be
unique, and (2) that the maximum area (1, 1, 2, 2) quadrilateral is the
(1+1=2, 2, 2) equilateral triangle of area sqrt 3, where the two edges of
length 1 make an angle of 180 degrees, and asks if that equilateral triangle
with a vertex in the middle of its side is really a quadrilateral, or is
that another ambiguity in equivalence of polygons under geometrical
similarity? He is also dubious that the integer-edged polygonal knots in R^3
are really polygons, as I've stated.

I agree with David Wilson's sequence.  What about a sequence table of
maximal areas of all simple integer-sided k-gons of perimeter n?

-- Jonathan Vos Post

On 10/24/06, David Wilson <davidwwilson at comcast.net> wrote:
>
> And we should have a sequence that counts all simple integer-sided
> polygons
> of perimeter n. Depending on exactly what we are counting, the sequence
> might go:
>
> a(3) = 1, the 1-1-1 triangle.
> a(4) = 1, the 1-1-1-1 quadrilateral.
> a(5) = 3, the 1-2-2 triangle, 1-1-1-2 quadrilateral, the 1-1-1-1-1
> pentagon.
>
> etc.
>
>
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