Can someone please explain the concept and theory behind this?? I’ve heard alot of nature and bees all add up to the ratio but im so confused as to why and whats the purpose.
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The Fibonacci sequence is a sequence starting with 0 and 1, in which the next term is always the sum of the previous two. The Golden ratio is usually what you hear about though when referring to nature, so lets define the golden ratio in terms of the Fibonacci sequence. Listing the first few terms it’d be [0 1 1 2 3 5 8 13 21 34]. A ratio is the amount of times one value is contained by another, also known as a division. So lets try going over the sequence dividing the current number by the previous.
0/1 = 0. 1/1 = 1. 2/1 = 2. 3/2 = 1.5. 5/3 = 1.67. 8/5 = 1.6. 13/8 = 1.625.
This will go on forever, as the Fibonacci sequence is of course infinite. But this division will continue to approach a value of about 1.618. This value is called the golden ratio, or Phi. Like Pi, it has an infinite number of non repeating digits.
Now, why does it appear in nature? Well, when Pi appears in nature its pretty clear why. Its something circular, and Pi is defined by the ratio of a circles circumference divided by its diameter. So if you have a circle, you have pi. With Phi its a bit trickier. The most common place we’ll see it is with things that spiral. Why is that? Well, lets look at another way to express the Golden Ratio, the Golden Rectangle and Spiral.
You can discover it yourself, following the instruction below. If you don’t want to, look up an image of Golden Squares/Spiral and you’ll see this effect.Take a piece of grind paper, and near the center draw a square around a single square. Do the same to the one directly right of it. Above them, draw a 2×2. You should now have a 2×3 rectangle. If we then draw a 3×3 square to the left of them, we now have a 5×3 rectangle. One more time above with a 5×5 square, and you’ll have a 5×8. Keep doing this, going counterclockwise the whole way . Notice how the dimensions of these squares form the Fibonacci sequence with there dimensions. Notice how they spiral outwards, getting larger and larger. If you draw a diagonal line across each square in the same counter clockwise motion, you’ll actually be able see that spiral begin to form. If you use a compass it’ll be even more clear. Seeing this, we can now redefine Phi not in terms of purely numbers, but in terms of something physical. The area of the 5×5 square we drew is 25. The rectangle it was placed next to was 5×3, an area of 15. If we divide 25/15, we get 1.666. If we repeat this, taking the area of the next square, and dividing by the total area we drew before, it will approach Phi!
Getting more real world, where could we see this in nature? Essentially anywhere in which things of a small size build up and spiral out like this we’ll be able to find it. Many flowers form spirals with there leaves or branches in this exact sort of way. They grow naturally in a spiral pattern, with future levels getting bigger. Many plants grow in this recursive way, simply because its efficient. The ratio then comes out naturally, just as Pi comes out naturally with circles. We don’t build tires intentionally to have the Pi ratio, but if you build a circular tire it will express Pi naturally.
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