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Problem leva in moža : delo diplomskega seminarja
ID Gruden, Klara (Author), ID Iršič, Vesna (Mentor) More about this mentor... This link opens in a new window

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Abstract
Problem moža in leva je klasični problem pregona in izmikanja, ki ga je leta 1930 predstavil nemško-britanski matematik Richard Rado. Postavlja vprašanje, ali lahko lev ujame moža v krožni areni, če se oba premikata z enako največjo hitrostjo. Kljub navidezni enostavnosti se je izkazalo, da je problem bolj kompleksen, kar je vodilo k več poskusom rešitve. Prvi poskus, imenovan pot pregona, predvideva, da lev teče naravnost proti možu, medtem ko ta teče po robu arene. V drugem poskusu rešitve, imenovanem pravilo polmera, lev sledi bolj prefinjeni strategiji, tako da ves čas ohranja položaj na enakem polmeru kot mož, ki teče po robu arene.Končno pravilna rešitev pa je Besicovitcheva strategija. Mož lahko s stalnim spreminjanjem smeri svoje poti nenehno beži pred levom, kar pomeni, da ga lev nikoli ne ujame. Problem se ni končal samo z osnovno različico, temveč so se razvile mnoge variacije. Problem je bil razširjen v višje dimenzije, postavljen v različne metrične prostore, obravnava lahko več levov ali pa moža, ki je hitrejši od levov. Prav tako lahko v prostoru dodamo ovire, kar problem še dodatno zaplete. Nekatere izmed teh različic še vedno ostajajo odprte za raziskovanje.

Language:Slovenian
Keywords:problem leva in moža, pot pregona, pravilo polmera, Besicovitcheva strategija
Work type:Final seminar paper
Typology:2.11 - Undergraduate Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2024
PID:20.500.12556/RUL-162011 This link opens in a new window
UDC:519.8
COBISS.SI-ID:208273923 This link opens in a new window
Publication date in RUL:18.09.2024
Views:89
Downloads:16
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Secondary language

Language:English
Title:Man and Lion
Abstract:
The man and lion problem is a classic pursuit and evasion problem, first introduced in 1930 by the German-British mathematician Richard Rado. It raises the question of whether a lion can catch a man in a circular arena if both move at the same maximum speed. Despite its apparent simplicity, the problem turned out to be more complex, leading to several attempts at solving it. The first attempt, called the pursuit path, assumes that the lion runs directly towards the man while the man runs along the edge of the arena.In the second solution attempt, known as the radius rule, the lion follows a more refined strategy by constantly maintaining its position at the same radius as the man, who runs along the edge of the arena. The final correct solution is Besicovitch's strategy. The man, by continuously changing the direction of his path, can infinitely evade the lion, meaning the lion never catches him. The problem didn't end with this basic version, as many variations have since been developed. The problem has been expanded into higher dimensions, different metric spaces, and can involve multiple lions or a man who runs faster than the lions. Obstacles can also be introduced into the space, making the problem even more complex. Some of these variations remain open for further exploration.

Keywords:man and lion problem, pursuit path, radius rule, Besicovitch's strategy

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