Question

Do some basic google research on the Fibonacci Sequence (also known as the golden mean and the golden ratio). The ratio itself is purely quantitative in nature. However, there’s no end to the interpretations of the meaning and significance of the numbers involved. Anything that involves examining the meaning of the formula is qualitative in nature. Once you’ve formulated an opinion as to why the Fibonacci Sequence exists or what it suggests, write 2-3 speculative paragraphs exploring your qualitative conclusions based on some very quantitative number crunching.

Answer 1

The Fibonacci sequence is the sequence that starts off 0,1,.. and every subsequent number is the sum of the two previous numbers. It continues: 0,1, 1, 2, 3, 5, 8,13, 21, 34, 55, ... The numbers start to get big after a while. These numbers are associated with spirals in plant life; for example, the spines on a cactus, the scales on a pineapple, or the seeds in a sunflower. The number of spiral rows in these instances are usually numbers in the Fibonacci sequence. This suggests that plant evolution has solved some kind of optimization problem by using Fibonacci numbers. Just what that optimization problem is, is an interesting question. The ratios of consecutive Fibonacci numbers approach 1.6180339... a number known as “phi”, which has an almost cult following among artists, architects, anatomists, aesthetics, and assorted alternative advocates. It's a pretty interesting number from a mathematical point of view, but that's getting off the topic.