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dc.contributor.authorPersinger, Carl Allanen_US
dc.date.accessioned2016-02-01T18:05:52Z
dc.date.available2016-02-01T18:05:52Z
dc.date.issued1962en_US
dc.identifier.urihttp://hdl.handle.net/10919/64732
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_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.publisherVirginia Polytechnic Instituteen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subject.lccLD5655.V855 1962.P477en_US
dc.subject.lcshFibonacci numbersen_US
dc.titleFibonacci sequencesen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreeMaster of Scienceen_US
dc.identifier.oclc22537570en_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Instituteen_US
thesis.degree.disciplineMathematicsen_US
dc.type.dcmitypeTexten_US


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