All Questions
7
questions
1
vote
1
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Polygon Diagonal Combinatorics
A diagonal for a polygon is defined as the line segment joining two non-adjacent points. Given an n-sided polygon, how many different diagonals can be drawn for this polygon?
I know that the number of ...
- 150
2
votes
1
answer
393
views
Number of isoceles triangles formed by the vertices of a polygon that are not equilateral
QUESTION: Let $A_1,A_2,...,A_n$ be the vertices of a regular polygon with $n$ sides. How many of the triangles $△A_iA_jA_k,1 ≤ i < j < k ≤ n,$ are isosceles but not equilateral?
MY APPROACH: ...
- 1,323
0
votes
1
answer
178
views
Number of ways to choose a closed path of given length on a square lattice
Also known as self-avoiding polygons, this is an unsolved problem. However, to leading order in the asymptotic limit, the number of polygons of a given perimeter scales exponentially with perimeter ...
- 1,191
4
votes
2
answers
5k
views
Ways to create a quadrilateral by joining vertices of regular polygon with no common side to polygon
How many ways are there to create a quadrilateral by joining vertices of a $n$- sided regular polygon with no common side to that polygon?
It's quite easy to solve for triangles for the same question,...
- 199
23
votes
4
answers
93k
views
How many triangles can be formed by the vertices of a regular polygon of $n$ sides?
How many triangles can be formed by the vertices of a regular polygon of $n$ sides? And how many if no side of the polygon is to be a side of any triangle ?
I have no idea where I should start to ...
- 335
22
votes
8
answers
3k
views
Number of ways to connect sets of $k$ dots in a perfect $n$-gon
Let $Q(n,k)$ be the number of ways in which we can connect sets of $k$ vertices in a given perfect $n$-gon such that no two lines intersect at the interior of the $n$-gon and no vertex remains ...
- 821
0
votes
0
answers
331
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Solving the "Library of Babel" puzzle, but for polygons.
The Library of Babel is a story about a universe whose contents are every possible 410-page book that could possibly exist. After a conversation with someone about doing this with images, and coming ...
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