![]() ![]() Perhaps the most famous example of all, the seashell known as the nautilus, does not in fact grow new cells according to the Fibonacci sequence, he added. Are there real-life examples of the Fibonacci sequence? "It's not 'God's only rule' for growing things, let's put it that way," Devlin said. But there are just as many plants that do not follow this rule. Pinecones exhibit a golden spiral, as do the seeds in a sunflower, according to " Phyllotaxis: A Systemic Study in Plant Morphogenesis" (Cambridge University Press, 1994). For instance, the spiral arrangement of leaves or petals on some plants follows the golden ratio. The golden ratio manages to capture some types of plant growth, Devlin said. ![]() Read more: The 9 most massive numbers in existence The ratio of successive numbers in the Fibonacci sequence gets ever closer to the golden ratio, which is 1.6180339887498948482. It's true that the Fibonacci sequence is tightly connected to what's now known as the golden ratio, phi, an irrational number that has a great deal of its own dubious lore. However, it's not some secret code that governs the architecture of the universe, Devlin said. Other than being a neat teaching tool, the Fibonacci sequence shows up in a few places in nature. (Image credit: Shutterstock) Why is the Fibonacci sequence important? The Fibonacci sequence and the golden ratio are eloquent equations, but they aren't as magical as they may seem. In 1877, French mathematician Édouard Lucas officially named the rabbit problem "the Fibonacci sequence," Devlin said. In fact, it was mostly forgotten until the 19th century, when mathematicians worked out more about the sequence's mathematical properties. But after a few scant paragraphs on breeding rabbits, Leonardo of Pisa never mentioned the sequence again. "Liber Abaci" first introduced the sequence to the Western world. Read more: 9 equations that changed the world The answer, it turns out, is 144 - and the formula used to get to that answer is what's now known as the Fibonacci sequence. (Ignore the wildly improbable biology here.) After a year, how many rabbits would you have? A month later, those rabbits reproduce and out comes - you guessed it - another male and female, who also can mate after a month. After a month, they mature and produce a litter with another male and female rabbit. The problem goes as follows: Start with a male and a female rabbit. In one place in the book, Leonardo of Pisa introduces the sequence with a problem involving rabbits. Written for tradesmen, "Liber Abaci" laid out Hindu-Arabic arithmetic useful for tracking profits, losses, remaining loan balances and so on, he added. However, in 1202 Leonardo of Pisa published the massive tome "Liber Abaci," a mathematics "cookbook for how to do calculations," Devlin said. (Image credit: Stefano Bianchetti/Corbis via Getty Images) ![]() However, in 1202 in a massive tome, he introduces the sequence with a problem involving rabbits. There are more examples of Fibonacci numbers in nature that we haven’t covered here.Portrait of Leonardo Fibonacci, who was thought to have discovered the famous Fibonacci sequence. … we see that each bump has bumps that form spirals, and each of those little bumps has bumps that form spirals! Hm, sounds like a fractal… There’s a vegetable called the romanesco, closely related to broccoli, that has some pretty stunning spirals.Īnd there’s more! Not only do the bumps form spirals, but if we look closely… Broccoli and cauliflower do, too, though it’s harder to see. You can find more examples around your kitchen! Pineapples and artichokes also exhibit this spiral pattern. Fibonacci can also be found in pinecones. This spiraling pattern isn’t just for flowers, either. If you’re feeling intrepid, count the spirals on that one and see what you get! Check out the seed head of this sunflower: ![]() See if you can find the spirals in this one!įibonacci spirals aren’t just for flower petals. (One of each is highlighted below.) Try counting how many of each spiral are in the flower – if you’re careful, you’ll find that there are 8 in one direction and 13 in the other. No, don’t start counting all the petals on that one! What we’re looking at here is a deeper Fibonacci pattern: spirals. Here’s a different kind of Fibonacci flower: For example, there’s the classic five-petal flower:īut that’s just the tip of the iceberg! Try counting the petals on each of these! The number of petals on a flower, for instance, is usually a Fibonacci number. As it turns out, the numbers in the Fibonacci sequence appear in nature very frequently. ![]()
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