20.500.12556/DKUM-10417 FIBONACCIJEVA ŠTEVILA FIBONACCI NUMBERS Zaporedje Fibonaccijevih števil je definirano z F0 = 0, F1 = 1 in za n≥2, Fn=F(n-1)+ F(n-2). Fibonaccijeva števila imajo dolgo in bogato zgodovino. Poznamo jih odkar je v začetku 13. stol. Leonardo Fibonacci postavil svoje znamenito vprašanje o razmnoževanju zajčkov. V tem diplomskem delu predstavljamo kombinatorični pristop k dokazovanju izrekov vezanih na Fibonaccijeva, Lucasova in Gibonaccijeva števila. Predstavljenih pa je tudi nekaj povezav med filotakso in zlatim rezom s Fibonaccijevimi števili. The Fibonacci numbers are defined by F0 = 0, F1 = 1 and for n≥2, Fn = F(n-1) + F(n-2). They have a long and rich history. They have served as mathematical inspiration and amusement since Leonardo Pisano first posed his original rabbit reproduction question at the beginning of the 13th century. In these Graduation Thesis we present combinatorial approach of proving Fibonacci, Lucas and Gibonacci identities. There are present relationships between golden section and phyllotaxis with Fibonacci numbers . matematika Fibonaccijeva števila Lucasova števila Gibonaccijeva števila kombinatorika filotaksa zlati rez. mathematic Fibonacci numbers Lucas numbers Gibonacci numbers combinatorics phyllotaxis golden section. true true false [S. Toplak] Slovenski jezik Angleški jezik Diplomsko delo 2009-05-13 12:44:51 2009-05-22 13:50:58 2022-04-11 16:15:45 2022-04-16 03:26:06 2009 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 16864776 URN:SI:UM:DK:CB0HHLWY UNI_Toplak_Stanislava_2009.pdf UNI_Toplak_Stanislava_2009.pdf 1 DD706793EDB1B059830ED3B34AF7B587 2d2603b898fbbe9fea5b4ff5a7f8603fcfe23cf43dddddb30b7eb51a5e40f25a d2c01664-7c02-11eb-bb7a-00155d0001ca 20.500.12556/dkum/35d56400-f8e9-4e38-9242-c359600aac4c https://dk.um.si/Dokument.php?lang=slv&id=8505 Fakulteta za naravoslovje in matematiko 0 0 0