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Non-standard Aspects of Fibonacci Type Sequences
; University of Technology Vienna, University of Technology Vienna,University of Technology Vienna,Vienna, Austria
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  or the cubic ˝plastic number" by VAN DER LAAN  resp. the ˝cubi ratio" by L. ROSENBUSCH . 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.
generalized Fibonacci sequence; Golden Mean; non-Euclidean geometry; number field; ring
Hrčak ID: 192219
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