worm in the plane
Source: Bundeswettbewerb Mathematik 1990, stage 2, problem 4
June 18, 2004
inequalitiesfunctiongeometry3D geometryspheregeometry solved
Problem Statement
In the plane there is a worm of length 1. Prove that it can be always covered by means of half of a circular disk of diameter 1.
Note. Under a "worm", we understand a continuous curve. The "half of a circular disk" is a semicircle including its boundary.