ABSTRACT
The history of Fibonacci numbers, their origin, and presence in many spheres of nature are described. Fibonacci was an Italian mathematician of the early 13th century. The name Fibonacci was a short for the Latin "filius Bonacci," which means "the son of Bonacci," but his real name was Leonardo Bonacci. Plant growth is governed by the Fibonacci sequence, which can be understood as a law of accumulation. With successively dividing each term in the Fibonacci sequence by the previous term, a ratio appears to be settling down to about a particular value (1.618034), which is called the golden ratio. The branching rates in plants occur in the Fibonacci pattern, where the first branch level has one branching (the trunk), the second has two branches, then 3, 5, 8, 13, and so on. The Fibonacci numbers appear in Phyllotaxis, to the pattern of the florets in inflorescence, the bracts of a pinecone, or the scales of a pineapple. In palms, leaves are spirally arranged in the clockwise or counterclockwise direction, and the number of spirals always follows the Fibonacci sequence. The total numbers of petals in many plants follow Fibonacci numbers. In a sunflower capitulum (seedhead) bearing equal-sized seeds, the numbers of visible spirals vary with the diameter of the disc, all matching with terms in the Fibonacci sequence. Recent studies, however, show that in most seedheads, spirals follow Fibonacci numbers but some are approximately Fibonacci, some without Fibonacci structure, and some parastichy numbers equal to one less than a Fibonacci number and in some, one more than a Fibonacci number. The Fibonacci spiral in the nautilus sea shell approximates the golden spiral, with squares whose side lengths vary by the golden ratio. Each one is an example of logarithmic spirals, very common in nature.
