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Omni-MATH / Let P be a convex polygon with n sides, n≥3. Any set of n minus{} 3 diagonals of P that do not intersect in the interior of the polygon determine a [i]triangulation[/i] of P into …

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problem

Let P \mathcal{P} be a convex polygon with n n sides, n≥3 n\ge3. Any set of $ n \minus{} 3$ diagonals of P \mathcal{P} that do not intersect in the interior of the polygon determine a [i]triangulation[/i] of P \mathcal{P} into $ n \minus{} 2$ triangles. If P \mathcal{P} is regular and there is a triangulation of P \mathcal{P} consisting of only isosceles triangles, find all the possible values of n n.
Plain-text mathematical notation (without MathML)
Let P be a convex polygon with n sides, n≥3. Any set of $ n \minus{} 3$ diagonals of P that do not intersect in the interior of the polygon determine a [i]triangulation[/i] of P into $ n \minus{} 2$ triangles. If P is regular and there is a triangulation of P consisting of only isosceles triangles, find all the possible values of n.
Original LaTeX notation
Let $ \mathcal{P}$ be a convex polygon with $ n$ sides, $ n\ge3$. Any set of $ n \minus{} 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 \minus{} 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$.

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Source and history

task_id
112a9fa4-f535-521b-98b4-d80489e5f752
task_key
test--112a9fa4-f535-521b-98b4-d80489e5f752
task_revision_id
1
config / split
/ test

Official source

initial import