On the Fibonacci Numbers
نویسنده
چکیده
The Fibonacci numbers are terms of the sequence defined in a quite simple recursive fashion. However, despite its simplicity, they have some curious properties which are worth attention. In this set of notes, we will look at some of the important features of these numbers. In the first half of the notes, our attention shall be paid to the relationship of the Fibonacci numbers and the Euclidean algorithm. The main theorem is that of Gabriel Lamé, which relates the complexity of the Euclidean algorithm with the Fibonacci numbers. In the second half of the notes, we will look at the Fibonacci numbers from linear algebraic point of view. Our treatment shall essentially be a glimpse of the more general theory of linear recurrence.
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