A translation of Henri Joris' "Le chasseur perdu dans la for\^et" (1980)

TL;DR

This paper provides an English translation of Henri Joris' 1980 article, detailing the geometric problem of finding the shortest search path to locate a line from a point with known distance but unknown direction.

Contribution

It offers a complete and detailed proof of the shortest search path problem originally described by Isbell, filling a gap in the published literature.

Findings

Provides the first detailed proof of the shortest search path problem

Clarifies geometric strategies for locating a line from a point

Enhances understanding of plane geometry search problems

Abstract

This is an English translation of Henri Joris' article "Le chasseur perdu dans la for\^et (Un probl\`eme de g\'eom\'etrie plane)" that appeared in $Elemente\ der\ Mathematik$ v. 35 (1980) n. 1, 1--14. Given a point $P$ and a line $L$ in the plane, what is the shortest search path to find $L$, given its distance but not its direction from $P$? The shortest search path was described by Isbell (1957), but a complete and detailed proof was not published until Joris (1980). I am thankful to Natalya Pluzhnikov for her dedicated work and to the Swiss Mathematical Society for permission to post this translation on the arXiv.