Geometry

   

Lost in an Isosceles Triangle

Authors: Philip Gibbs

Sixty years ago Richard Bellman issued a difficult challenge to his fellow mathematicians. If a rambler is lost in a forest of known shape and size, how can she find the best path to follow in order to escape as quickly as possible? So far solutions are only known for a handful of simple cases and the general problem has therefore been described as “unapproachable.” In this work a computational “random paths” method to search for optimal escape paths inside convex polygonal forests is described. In particular likely solutions covering all cases of isosceles triangles are given. Each conjectured solution provides a potentisl upper-bound for Moser’s worm problem. Surprisingly there are two cases of triangles which would provide improvements on the best known proven upper bounds.

Comments: Pages. DOI: 10.13140/RG.2.2.13171.12325

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Submission history

[v1] 2016-07-02 02:33:06

Unique-IP document downloads: 111 times

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