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visits member for 3 years, 6 months
seen Nov 6 '13 at 3:42

Feb
20
asked Linear Algebra of Symmetric Sums
Feb
18
accepted For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
Feb
18
awarded  Quorum
Feb
12
comment Unique characterization of convex polygons
@Don: You may want to look at the second and third section of my answer. Section two is a very simple approach to selecting a distinguished vertex. Section three is an more complete (but not quite finished) version of the centroid approach to selecting a first vertex. You are right the centroid approach is a bit unstable. It is also very complicated to apply to all cases.
Feb
11
comment For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
@ Christian: Cool! Your box function may provide a way to explore the second half of my question.
Feb
11
revised For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
added 16 characters in body
Feb
11
comment For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
@Christian: Interesting. However, your counter-example is consistent with the pseudo-proof, so I'm not worried yet. Assume for the lemma that the polygon is convex. I've edited the question ... but for non-convex polygons, maybe I should look at moments instead.
Feb
11
revised For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
added 9 characters in body
Feb
11
awarded  Supporter
Feb
11
asked For a polygon on complex plane, when are the vertex 'Fourier coefficients' non-zero
Feb
11
comment Unique characterization of convex polygons
@Don: If you add the feature point as a vertex, it is arbitrary between which two vertices you put it. So you must choose a second vertex. If you treat the feature point separately, you must choose a first vertex for your polygon. Unfortunately, cyclic re-orderings of vertices change your $C(P)$. For example $P=(\sqrt{2},e^{i\frac{3\pi}{4}},e^{i\frac{5\pi}{4}})$ and $P'=(e^{i\frac{3\pi}{4}},e^{i\frac{5\pi}{4}},\sqrt{2})$ are the same polygon, but $C(P)\neq C(P')$. So either way, you need to choose a first(second) vertex in a way that you always choose equivalent vertices in congruent polygons.
Feb
10
comment Unique characterization of convex polygons
Given that the OP has apparently allowed the feature point to be any interior point in the polygon, if you add it to the polygon as a distinguished vertex, you will end up with a non-convex polygon. As a result, there may not be a unique counter clock-wise ordering of the vertices. Won't that be a problem? Alternatively, if you deal the featured point separately from the polygon, you have to choose a distinguished vertex of the polygon in such a way that you always choose equivalent vertices in congruent polygons.
Feb
4
revised $ \biggl\lfloor{\frac{x}{1!}\biggr\rfloor} + \biggl\lfloor{\frac{x}{2!}\biggr\rfloor} + \cdots \biggl\lfloor{\frac{x}{10!}\biggr\rfloor}=1001$
added 30 characters in body
Feb
4
answered $ \biggl\lfloor{\frac{x}{1!}\biggr\rfloor} + \biggl\lfloor{\frac{x}{2!}\biggr\rfloor} + \cdots \biggl\lfloor{\frac{x}{10!}\biggr\rfloor}=1001$
Jan
28
awarded  Commentator
Jan
28
comment In neutral geometry, can a family of parallel lines leave holes in the plane?
Epilogue: Now, suppose we have family of parallel lines all at angle $\alpha (≠ 90)$ to line $l$. Do they pass through every point on the plane? With the angle sum theorem this is easy. Without it, ... hmm? I've got a limiting process which looks like it will work. If you like this sort of stuff, see what you can do.
Jan
28
comment In neutral geometry, can a family of parallel lines leave holes in the plane?
Thank you. I'll try to find that. I'm working with an unpublished manuscript by Jack Lee. It's very clear and readable. It should published someday.
Jan
28
revised In neutral geometry, can a family of parallel lines leave holes in the plane?
added 4 characters in body
Jan
28
revised In neutral geometry, can a family of parallel lines leave holes in the plane?
added 455 characters in body
Jan
28
awarded  Scholar