Because of the relationship between the Fibonacci numbers and the golden ratio, the Fibonacci spiral eventually converges to the golden spiral. You will recognize the Fibonacci spiral …

We will look at a few interesting mathematical properties of Fibonacci numbers that are related to this course. In particular, using eigenvalues, eigenvectors, and a bit of algebra, we can find an …

We will prove Conjecture 1 by analyzing the greatest common divisor of Fibonacci numbers. We will prove a partial result regarding the values of ap for all primes p (see Corollary 4). For …

Fibonacci num-bers are found to be “prevalent” in the phyllotaxis of various trees, in seed heads, pinecones, and sunflowers. It is still an ongoing effort by botanists and applied mathematicians …

Each term of the Fibonacci sequence can be represented with a square whose sides have a length equal to the value of the corresponding term. If one takes all of the squares from the …

Fibonacci sequence. The Fibonacci sequence is recursi. n 1 + Fn 2 for n 2: Theorem 2.2.4 looks at the sum of the Fibonacci number. with even indices. Returning to the technique used in …

Fibonacci used the sequence named after him to discuss a problem concerning reproduction of rabbits. Assume that a pair (one male and one female) of rabbits takes a month to reach …