![]() ![]() Most other alleged occurrences of Fibonacci in nature are bogus. Some pattern that emerges repeatedly in the natural world is the Fibonacci Sequence. The connection between Fibonacci numbers, certain spirals, the golden number and the structure of many plants is genuine and increasingly well understood. Others say it underlies everything from natures patterns to beauty in art and. In particular, most have two arms winding from the centre, whereas the logarithmic spiral has a single arm. Some say its the most mythical number in the universe. If you take any two successive numbers from the sequence, their ratio is very close to that of the golden ratio. ![]() The spirals of galaxies are not even logarithmic. The sequence starts at 0 and 1, with the sequence continuing as 0, 1, 1, 2. The connection with elephant tusks is pretty much non-existent. The Fibonacci Sequence is a series of numbers, where each number in the sequence is the sum of the two previous numbers. The spirals in horns have even less to do with Fibonacci. ![]() This growth rate is different in different gastropod species. The usual “Fibonacci” spiral has a growth rate of about 6.8 – the fourth power of the golden number – whereas that of the nautilus is about 3, meaning it is too tightly wound to be related to Fibonacci. However, it's not some secret code that governs the architecture of the universe, Devlin said. In such spirals the space between consecutive windings grows exponentially at a fixed rate, and this rate can be any positive number. Other than being a neat teaching tool, the Fibonacci sequence shows up in a few places in nature. Unfortunately the correlation ends there, because there are many different logarithmic spirals. And the nautilus shell does have the form of a logarithmic spiral. It is true that the Fibonacci numbers are associated with a particular kind of spiral – the logarithmic spiral – and they are also closely associated with the “golden number”, which is roughly 1.6. The illustrations shown however use a true Golden Spiral, which is based on successive golden rectangles whose sides are already in the ratio of 1.618 to 1. Your point is valid that a Fibonacci spiral approximate the Golden Spiral as the numbers grow. Gael Mariani and Martin Scott perpetuate a series of myths in their letter about Fibonacci numbers in nature (3 September, p 19). This article does NOT use the Fibonacci sequence to draw the golden spiral. ![]()
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