All Questions
Tagged with polygons combinatorics
66
questions
1
vote
1
answer
195
views
Corresponding Triangulations of an (n+2)-gon to n Segments Connecting n+1 Collinear Points
So I'm asked to count the number of ways of connecting n+1 collinear points with n line segments subjected to the following constraints:
If the line is L
1) No segment passes below L.
2) Starting at ...
- 4,093
4
votes
1
answer
2k
views
How many triangles are formed by $n$ chords of a circle? [duplicate]
This is a homework problem I have to solve, and I think I might be misunderstanding it. I'm translating it from Polish word for word.
$n$ points are placed on a circle, and all the chords whose ...
- 6,315
9
votes
2
answers
432
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Why does the term ${\frac{1}{n-1}} {2n-4\choose n-2}$ counts the number of possible triangulations in a polygon?
In the given picture bellow, it counts the number of different triangloations in a polygon, how do the get to this expression, why is it:
$$
{2n-4\choose n-2}
$$
and why do we multiply it by $${\...
- 1,661
1
vote
1
answer
356
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Find the minimal number of guard points of polygon
Given a polygon with $n$ vertices, what is the minimal number of points inside the polygon such that for each interior point there exists at least one point such that the segment between them lies ...
- 4,793
1
vote
2
answers
439
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Property of nonconvex polygons
How to prove that each non-convex polygon with no self-intersecting parts, has at least one interior angle which size is less then $180$ degrees.
- 4,793
0
votes
0
answers
547
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k-dissection of a polygon with non-intersecting diagonals
I am trying to use the vertex coalescing method like the one mentioned here, page 10, to count: Number of dissections of a polygon using non-intersecting diagonals into even number of regions.
I am ...
- 1