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dc.contributor.authorPersinger, Carl Allanen
dc.date.accessioned2016-02-01T18:05:52Zen
dc.date.available2016-02-01T18:05:52Zen
dc.date.issued1962en
dc.identifier.urihttp://hdl.handle.net/10919/64732en
dc.description.abstractEarly in the thirteenth century, Leonardo de Pisa, or, Fibonacci, introduced his famous rabbit problem, which may be stated simply as follows: assume that rabbits reproduce at a rate such that one pair is born each month from each pair of adults not less than two months old. If one pair is present initially, and if none die, how many pairs will be present after one year? The solution to the problem gives rise to a sequence {Un} known as the Classical Fibonacci Sequence. {Un} is defined by the recurrence relation Un = Un-1 + Un-2, n ≥ 2, U₀ = 0, U₁ = 1 Many properties of this sequence have been derived. A generalized sequence {Fn} can be obtained by retaining the law of recurrence and redefining the first two terms as F₁ = p', F₂ = p' + q' for arbitrary real numbers p' and q'. Moreover, by defining H₁ = p+iq, H₂ = r+is, p,q,r and s real, a complex sequence is determined. Hence, all the properties of the classical sequence can be extended to the complex case. By reducing the classical sequence by a modulus m, many properties of the repeating sequence that results can be derived. The Fibonacci sequence and associated golden ratio occur in communication theory, chemistry, and in nature.en
dc.format.extent58 leavesen
dc.format.mimetypeapplication/pdfen
dc.language.isoen_USen
dc.publisherVirginia Polytechnic Instituteen
dc.relation.isformatofOCLC# 22537570en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V855 1962.P477en
dc.subject.lcshFibonacci numbersen
dc.titleFibonacci sequencesen
dc.typeThesisen
dc.contributor.departmentMathematicsen
dc.description.degreeMaster of Scienceen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelmastersen
thesis.degree.grantorVirginia Polytechnic Instituteen
thesis.degree.disciplineMathematicsen
dc.type.dcmitypeTexten


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