ERIC Number: EJ771158
Record Type: Journal
Publication Date: 2007-Jul
Reference Count: 7
Simons, C. S.; Wright, M.
International Journal of Mathematical Education in Science and Technology, v38 n5 p677-682 Jul 2007
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.
Descriptors: Mathematical Concepts, Mathematics Education, Algebra, Mathematical Applications, Sequential Approach, Validity, Mathematical Logic, Equations (Mathematics)
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Publication Type: Journal Articles; Reports - Evaluative
Education Level: N/A
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