journal of science education

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Classroom

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science.

Fibonacci Numbers, Seating Arrangements and Stair-climbing

Somnath Basu

We obtain different identities involving the Fibonacci numbers including the well-known Binet formula. It turns out that every positive integer can be expressed as a sum of distinct Fibonacci numbers. Fibonacci numbers have divisibility properties with some interesting consequences. For example, the GCD of two Fibonacci numbers is itself a Fibonacci number. We discuss matrices formed by these GCDs; they turn out to be positive definite. Finally, we consider combinatorial interpretations of a number of identities.

Address for Correspondence
Somnath Basu 
B. Math. Hons. IInd year 
Indian Statistical Institute 
Mysore Road Bangalore 560 059, India.

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