The Fibonacci sequence is a numerical sequence starting at 0 or 1, with the next number being the sum of the preceding two numbers. Counting that down gives you 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. The idea dates back into ancient India and maybe a few rather bright cave-man figured it out by observation as well. The latter might be true (although unlikely) because this sequence can be observed in a great deal of natural structures like plants, seed heads and shells.
What the advantage of this sequence is becomes evident if you image to be a plant with a lot of leaves, confronted with the task to order your leaves in a way that they take up the most sunlight and stop overshadowing one another. That is of course nothing else but a form of natural selection, because those plants that succeed will have more energy, more offspring and will dominate the gene pool.
So, if evolution figured out that this is the best way to order a large number of parts, how come that we don’t learn from that? The first time I encountered somebody smart enough to apply this insight to a photovoltaic installation, it was a 13 year-old boy ! This is a great example of human preoccupation with straight lines and ‘efficient’ design instead of ‘effective’ design. (A thought on the side: if you watch the video, notice the enormous amount of good-will and affection the boy receives. Would that be the same if the presenter was an adult? Probably not. Just think about the implications of that….)
Next to solar panel design, there are other areas in which the sequence might be of greater use. Think about ventilation, storage or computation – a field in which the sequence is well known in e.g. search algorithms. Another group of interested Fibonacci fans are artists, as they make use of our natural acquaintance with the sequence (so many trees have it build in) that forms in the same sequence are found to be more aesthetic than many artificial forms.