![]() As random as nature may appear at times, occasionally there is an underlying order. ![]() If you place squares next to one another in which each new square has the width of the next number in the Fibonacci sequence, the resulting formation is a spiral that appears exactly in the nautilus - and in the spiral of hurricanes. Perhaps the most famous example of all is the Fibonacci sequence expressed in the nautilus shell. 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. In approximating this rationally, we arrive at the ratio of two Fibonacci numbers: So, we can see that as the number of leaves. Since this is over half of the circle, we subtract this from one to get 1/ (phi2), or about 0.382. Your point is valid that a Fibonacci spiral approximate the Golden Spiral as the numbers grow. In the case of a 137.5-degree divergence angle, the ratio is 1/phi, which is approximately 0.618, as we saw here. For example, the distance between the tips of a starfish’s arms compared to distance from tip to tip across the entire body is very close to the golden ratio, and the eye, fins and tail of dolphins all fall at points along the dolphin’s body that correspond to the ratio. This article does NOT use the Fibonacci sequence to draw the golden spiral. Yet, the golden ratio is far more common among all living creatures, including those in the sea. So where do these show up in the ocean? For one, the Fibonacci numbers themselves are common: Sea stars and sand dollars, for example, have five points, while squids and octopuses have eight arms. ![]() As the series increases, the ratio of any two consecutive Fibonacci numbers becomes increasingly closer to the “golden ratio,” which is approximately 1.618. Though the numbers look random at first - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… - they actually follow a simple pattern: the next term in the series is the sum of the previous two terms. Credits: Raiana Tomazini-Wikipedia, Wikipedia, NASA A Fibonacci spiral, a nautilus shell cut in half, and a hurricane all share links to Fibonacci numbers.
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