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MMO 066 Moscow MO 1940 curve’s self-intersections unfolidng an infinite cone

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July 18, 2019
combinatorial geometrygeometrycone3D geometry

Problem Statement

* Given an infinite cone. The measure of its unfolding’s angle is equal to α\alpha. A curve on the cone is represented on any unfolding by the union of line segments. Find the number of the curve’s self-intersections.