A Mathematical Game of Reaching an Island in a Deep Lake with the Aid of a Rope

Abstract

The problem of reaching an island in a deep lake by a man who cannot swim, with the help of just a rope, has been generalised. The rope is such that it can be used to tie the two trees only, one on the edge of the lake and other in the island. The least length of the rope that the man would require has been obtained. The particular case of an elliptical lake with one tree at an end of a latus rectum and the other at the corresponding focus in an island there has been discussed.