Nestandardni pristupi nizovima Fibonaccijevog tipa

Autor:	Gunter Weiss
Jazyk:	angličtina
Rok vydání:	2017
Předmět:	Combinatorics Ring (mathematics) popćeni Fibonaccijev niz zlatni rez neeuklidska geometrija polje brojeva prsten Fibonacci number generalized Fibonacci sequence Golden Mean non-Euclidean geometry number field ring Non-Euclidean geometry Type (model theory) Algebraic number field Mathematics
Zdroj:	KoG Volume 21 Issue 21
ISSN:	1846-4068 1331-1611
Popis:	Fibonacci sequence and the limit of the quotient of adjacent Fibonacci numbers, namely the Golden Mean, belong to general knowledge of almost anybody, not only of mathematicians and geometers. There were several attempts to generalize these fundamental concepts which also found applications in art and architecture, as e.g. number series and quadratic equations leading to the so-called ˝Metallic means" by V. DE SPINADEL [8] or the cubic ˝plastic number" by VAN DER LAAN [5] resp. the ˝cubi ratio" by L. ROSENBUSCH [7]. The mentioned generalisations consider series of integers or real numbers. ˝Non-standard aspects" now mean generalisations with respect to a given number field or ring as well as visualisations of the resulting geometric objects. Another aspect concerns Fibonacci type resp. Padovan type combinations of given start objects. Here it turns out that the concept ˝Golden Mean" or ˝van der Laan Mean" also makes sense for vectors, matrices and mappings. Fibonaccijev niz i zlatni rez, limes kvocijenata susjednih Fibonaccijevih brojeva, su pojmovi poznati ne samo matematičarima i geometričarima, već gotovo svima. Oni svoju primjenu nalaze u umjetnosti i arhitekturi. Poznato je nekoliko pokušaja poopćenja ovih pojmova, kao što su nizovi brojeva i kvadratne jednadzbe koje rezultiraju takozvanim ˝metalnim rezovima" V. DE SPINADEL [8], ili kubni ˝plasticni broj" VAN DER LAANA [5], odnosno ˝kubni omjer" L. ROSENBUSCHA [7]. Spomenuta se poopćenja odnose na nizove cijelih ili realnih brojeva. ˝Nestandardnim pristupima" ovdje smatramo poopćenja u odnosu na dano polje ili prsten brojeva, kao i na vizualizaciju dobivenih geometrijskih objekata. Idući se pristup odnosi na Fibonaccijev, odnosno Padovanov tip kombinacija danih početnih objekata. Pokazuje se da pojam zlatnog reza ili van der Laanovog reza ima smisla promatrati i za vektore, matrice i preslikavanja.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a6828782e36ef53a9dc4dd31ce09064c https://hrcak.srce.hr/file/283540 Zobrazit plný text záznamu