The Fibonacci Sequence is a simple number pattern that goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... Can you see the pattern? The next number in the sequence is always the sum of the last two added together. Start with 1. It's the first number in the sequence so you can't add anything to it, so the next number's also 1. after that, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, and so on. So why is this number pattern such a big deal? Well, you'd be surprised how many awesome properties it has, but first, here's some history. The Fibonacci Sequence was, unsurprisingly, invented by someone named Fibonacci about 800 years ago. His full name was Leonardo Pisano Bigollo (Pisano means "from Pisa"), but he was also known as Leonardo of Pisa, and of course, Fibonacci, which means son of Bonacci. He came up with this starting with a problem about rabbits. You have a pair of baby rabbits. It takes them one month to mature and then start mating, and another month before the birth of another pair of baby rabbits (with the same properties). If no rabbits die, how many will there be in a year? (source) This may be a little confusing, so here's a picture to help you out:
Many plants have leaves, flowers, petals, branches, and more that are grouped in Fibonacci numbers. This is because it provides the most efficient way to make energy, or more specifically, collect sunlight, and doesn't create awkward gaps or overlaps. Why exactly? That has to do with an amazing number, phi. One Fibonacci number divided by the one before it gives you a number close to phi, an irrational number that is 1.618... The higher in the sequence you go, the closer to phi you get. The most ideal way for leaves to grow on a plant would be to always grow the next leaf a phi'th of a circle away from the one before it. This would create no direct overlaps, and it works good with any number of leaves there could be, which is good for plants because they keep growing new leaves. Unfortunately, plants can't handle complicated numbers like phi, so they use fractions made of Fibonacci numbers instead, so they can get close to phi. You can find Fibonacci numbers in plants everywhere, although I don't know ho they help in things that aren't leaves. Spirals are found in groups of Fibonacci numbers in things like pine cones and pineapples and flower seed arrangements. If you have a pine tree, then grab a pine cone and get to counting. This is my favorite way to find Fibonacci numbers in nature because it never not works and it's easy. Counting flower petals is easier, but it doesn't always work. I have this bush with flowers that actually have 6 petals on them. Anyway, on the pine cone, there will be some spirals going in one direction parallel to each other, and then more spirals going the other direction. Count each group of spirals, and they should be consecutive Fibonacci numbers, like 5 and 8. So one group has 5 spirals and the other has 8, or 3 and 5, or 8 and 13. No matter what this should always work out. The size of the pine cone doesn't even matter because that only affects the length of the spirals. For pineapples the pattern is very similar, but they have an extra, third set of spirals that goes almost straight up. It will have the next highest Fibonacci number of spirals after the other two sets of spirals. So if you have 8 and 13 in the first two groups, then the third will have 21 spirals. Fibonacci spirals can also appear in the seed arrangements of large flowers like sunflowers. Now that you know all about Fibonacci numbers in nature, go outside and look for more! Also here are three videos from the YouTube channel, Vihart, with plenty of info on Fibonacci numbers in nature.
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