Fibonacci Imposters
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| Title: | Fibonacci Imposters |
|---|---|
| Language: | English |
| Authors: | Simons, C. S., Wright, M. |
| Source: | International Journal of Mathematical Education in Science and Technology. Jul 2007 38(5):677-682. |
| Availability: | Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html |
| Peer Reviewed: | Y |
| Page Count: | 6 |
| Publication Date: | 2007 |
| Document Type: | Journal Articles Reports - Evaluative |
| Descriptors: | Mathematical Concepts, Mathematics Education, Algebra, Mathematical Applications, Sequential Approach, Validity, Mathematical Logic, Equations (Mathematics) |
| DOI: | 10.1080/00207390701228401 |
| ISSN: | 0020-739X |
| Abstract: | With Simson's 1753 paper as a starting point, the current paper reports investigations of Simson's identity (also known as Cassini's) for the Fibonacci sequence as a means to explore some fundamental ideas about recursion. Simple algebraic operations allow one to reduce the standard linear Fibonacci recursion to the nonlinear Simon's recursion that is equivalent to Simson's identity and then further to a nonlinear recursion dependent only on a single preceding term. This leads to a striking nonrecursive characterization of Fibonacci numbers that is much less well-known than it should be. It is then discovered that Simson's recursion itself implies a family of linear recursions and characterizes a class of generalized Fibonacci sequences. |
| Abstractor: | Author |
| Number of References: | 7 |
| Entry Date: | 2007 |
| Accession Number: | EJ771158 |
| Database: | ERIC |
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| Abstract: | With Simson's 1753 paper as a starting point, the current paper reports investigations of Simson's identity (also known as Cassini's) for the Fibonacci sequence as a means to explore some fundamental ideas about recursion. Simple algebraic operations allow one to reduce the standard linear Fibonacci recursion to the nonlinear Simon's recursion that is equivalent to Simson's identity and then further to a nonlinear recursion dependent only on a single preceding term. This leads to a striking nonrecursive characterization of Fibonacci numbers that is much less well-known than it should be. It is then discovered that Simson's recursion itself implies a family of linear recursions and characterizes a class of generalized Fibonacci sequences. |
|---|---|
| ISSN: | 0020-739X |
| DOI: | 10.1080/00207390701228401 |
