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Hank Green: Math wasn't made up to harass English majors, it was invented by a little something called nature, and it's everywhere you look.  In fact, there are specific numbers that we see in nature all the time.  Together, they're called the Fibonacci sequence and it goes something like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.  You may know this pattern, the first and the second add up to the third, and the second and the third add up to the fourth, and the fourth and the fifth add up to the sixth and so on.  The sequence was first described by mathematicians in India about 1300 years ago, and it was introduced to the west in 1202 by Leonardo of Pisa, aka Fibonacci, who was also responsible for introducing Arabic numerals to Europe, which, yeah, if he hadn't done that, we'd still be counting in Roman numerals, which would be terrible.  

Fibonacci was a mathematician, and in his book, Liber Abaci , he described this sequence with a thought-experiment about a family of incestuous bunnies.  If you put one boy bunny and one girl bunny together, that's two, and those two together will make a third, and those three, when they're done, you know, taking turns, will make five, et cetera.  But the easiest place to find these numbers in nature isn't in bunnies, it's in plants.  If you cut a banana into slices, you'll see that it has three distinct sections, an apple has five, no matter what kind of flower you're looking at, chances are, it has three, five, eight, 13, or 21 petals.  Rows of seeds in sunflowers and pine cones always add up to Fibonacci numbers.  Now, plants don't grow this way because they're receiving some kind of mysterious cosmic mandate, they're doing it because it's the most efficient way to pack as many seeds as possible into a small space, and if you want to see why that is, you can go watch Vi Hart's video, which is linked in the description and it's awesome.

But in addition to the numbers themselves, you also see the same ratio between Fibonacci numbers showing up.  So, when you divide almost any Fibonacci number by the one before it in the sequence, especially the larger ones, you get the same number, 1.618 dot dot dot, whoa, lots of numbers.  The Greeks discovered this long before Fibonacci, and they called it Phi, today, it's sometimes known as the Golden Ratio.  Phi was purportedly used by the Ancient Greek sculptor Phidias to illustrate the idea of physical perfection.  He is said to have used Phi as a ratio between a statue's total height and the distance from the bottom of its feet to its navel, for instance.  And also, the length of a face divided by its width.  There's a whole other set of patterns in nature that are based on what's called the Golden Rectangle, a rectangle whose side lengths are successive Fibonacci numbers like 8x13.  This rectangle can be divided up into a series of squares whose lengths are also successive Fibonacci numbers, in this case, 1x1, 2x2, 3x3, 5x5 and 8x8.  When you draw an arc from one corner of each square to the other, they join to form a spiral that resembles many of the spirals we observe in nature, from the unfolding leaves of a desert succulent, the arrangement of those pine cone lobes and sunflower seeds, and the shells of some snails, the math, you guys, it can be beautiful, too.

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