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Omni-MATH / ( Gregory Galparin ) Let P be a convex polygon with n sides, n≥3 . Any set of n−3 diagonals of P that do not intersect in the interior of the polygon determine a triangulation of P…

Problem

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problem

( Gregory Galparin ) Let P\mathcal{P} be a convex polygon with nn sides, n≥3n\ge3 . Any set of n−3n - 3 diagonals of P\mathcal{P} that do not intersect in the interior of the polygon determine a triangulation of P\mathcal{P} into n−2n - 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 nn .
Plain-text mathematical notation (without MathML)
( Gregory Galparin ) Let P be a convex polygon with n sides, n≥3 . Any set of n−3 diagonals of P that do not intersect in the interior of the polygon determine a triangulation of P into n−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
( 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 triangulation 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 $n$ .

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Source and history

task_id
e0f3ff31-f779-5800-8352-f576dff4ee67
task_key
test--e0f3ff31-f779-5800-8352-f576dff4ee67
task_revision_id
5
config / split
/ test

Official source

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