5
Problems(2)
treasure hunting by a mathematician , inside a circular island of radius 1
Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p5
9/19/2020
A treasure is buried at some point on a round island with a radius of km. On the coast of the island there is a mathematician with a device that indicates the direction to the treasure when the distance to the treasure does not exceed m. In addition, the mathematician has a map of the island, on which he can record all his movements, perform measurements and geometric constructions. The mathematician claims that he has an algorithm for how to get to the treasure after walking less than km. Could this be true?(B. Frenkin)
geometrydistancecircle
any convex polyhedron has three edges that can be used to form a triangle.
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p5
9/14/2020
Prove that any convex polyhedron has three edges that can be used to form a triangle.(Barbu Bercanu, Romania)
convexgeometrypolyhedron