Matrika - Jan Malej: Problem požrešne koze

Izbrane teme sodobne fizike in matematike

Problem požrešne koze

Članek predstavi problem požrešne koze in njegovo naravno posplošitev v \(n\)-razsežni evklidski prostor. Rešitev problema v ravnini je izražena implicitno in s pomočjo kompleksne analize tudi eksplicitno. Rešitve problemov v višjih razsežnostih so opisane implicitno s sistemom dveh enačb. Obravnavano je tudi limitno obnašanje rešitev, ko razsežnost prostora narašča preko vseh mej.

The grazing goat problem

The article presents the grazing goat problem and its natural generalization to the \(n\)-dimensional Euclidean space. The solution of the problem in the plane is expressed implicitly and explicitly, the latter using complex analysis. Solutions of the problems in higher dimensions are described implicitly with the system of two equations. The limiting behaviour of solutions as the dimension approaches infinity is also discussed.

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