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  The Golden Ratio in NatureHave you ever picked up a pine cone and noticed that the scales of the cone are in spirals that run both clockwise and counter-clockwise? If you haven't ever noticed that, pick up a cone and take a look sometime. You'll see what I mean.What's really interesting about these spirals is that in one direction you'll likely count five spirals, while in the other direction you'll count eight spirals. And the ratio 8:5 is 1.6, which is quite close to The Golden Ratio (approximately 1.618). "So what," you say. "That's just an odd coincidence, and doesn't mean anything." And I say, "Good for you. Be skeptical. What I've told you so far isn't enough to draw any sweeping generalizations. But let me tell you some more." Take a look at a pineapple. It also has spirals: eight in one direction, thirteen in the other. 13:8 = 1.625, which is even closer to The Golden Ratio. But here's the real kicker: take a look at a sunflower. You'll likely find that its opposing spirals come in one of the following ratios: 55:34, 89:55, or 144:89. Calculate those ratios and you find that they are approximately, in order: 1.61765, 1.61819, and 1.61798. These numbers are extraordinarly close to The Golden Ratio, which is approximately 1.61803. No wonder architects and artists thought this was an aesthetically pleasing ratio: the natural world uses this ratio over and over again! On the next page you can find a way that this number appears in mathematics.
Contents copyright 2008 by Douglas Twitchell. Contents of this page may not be reproduced without permission of the author.
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