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The Matrix Connection: Fibonacci and Inductive Proof

Tamara Veenstra, Catherine Miller 

January 2006, Volume 99, Issue 5, Page 328

Abstract:
This article presents several activities (some involving graphing calculators) designed to guide students to discover several interesting properties of Fibonacci numbers. Then, we explore interesting connections between Fibonacci numbers and matrices; using this connection and induction we prove divisibility properties of Fibonacci numbers. Includes problems and samples of tasks used to help student discover patterns within the Fibonacci Sequence and connections to matrix algebra.

Keywords:
Matrix Algebra
Calculators
Article
Conceptual Development
Grades 9-12
Math Coordinator / Coach
Teacher
Lesson Plans
Reasoning and Proof
Sequences / Series