Difference between revisions of "2008 USAMO Problems/Problem 4"

(create template)
 
(Fixed link)
Line 12: Line 12:
 
{{USAMO newbox|year=2008|num-b=3|num-a=5}}
 
{{USAMO newbox|year=2008|num-b=3|num-a=5}}
  
* <url>Forum/viewtopic.php?t=202905 Discussion on AoPS/MathLinks</url>
+
* <url>viewtopic.php?t=202905 Discussion on AoPS/MathLinks</url>

Revision as of 19:57, 1 May 2008

Problem

(Gregory Galparin) Let $\mathcal{P}$ be a convex polygon with $n$ sides, $n\ge3$. Any set of $n - 3$ diagonals of $\mathcal{P}$ that do not intersect in the interior of the polygon determine a [i]triangulation[/i] of $\mathcal{P}$ into $n - 2$ triangles. If $\mathcal{P}$ is regular and there is a triangulation of $\mathcal{P}$ consisting of only isosceles triangles, find all the possible values of $n$.

Solution

Solution 1

Solution 2

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

Resources

2008 USAMO (ProblemsResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6
All USAMO Problems and Solutions
  • <url>viewtopic.php?t=202905 Discussion on AoPS/MathLinks</url>
Invalid username
Login to AoPS