20.500.12556/RUL-162011 Problem leva in moža delo diplomskega seminarja Man and Lion 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. 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. problem leva in moža pot pregona pravilo polmera Besicovitcheva strategija man and lion problem pursuit path radius rule Besicovitch's strategy true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2024-09-18 08:15:36 2024-09-18 08:15:43 2024-09-20 08:49:04 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.8 143629 208273923 14541.pdf 14541.pdf 1 3527CFFAD56878E0DCE74E28FCCF3640 281e458f27c697f6a4115ed7d131b08e69b55a1b7b7e96bf6bfa92b82b499080 550aef02-7585-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=191025 Fakulteta za matematiko in fiziko 0 0 0