Okay, so I have not yet learned to stop worrying (pretty sure that’s just a lifetime commitment), but anyone who knows me knows that I LOVE the Fibonacci sequence! One of my favorite pieces of jewelry is this Fibonacci spiral necklace:
Above: Fibonacci necklace by Agate and Elm on Etsy
I always know that I’ve met a kindred spirit/fellow math nerd when someone comments on it, and I wear it every chance I get (or at least, when it goes with my outfit). So why do I love the Fibonacci sequence so much?
First of all, some of you may be wondering - what is the Fibonacci sequence? And how does it turn into that cool spiral? Quite simply, the Fibonacci sequence starts with 0 and 1; every number that follows in the sequence is the sum of the two numbers before it, like so:
If you were to stack squares made up of these numbers on top of and next to each other to form a rectangle, it would look like this:
If you connect those corners with a curved line, you get this beautiful spiral:
(Okay, so those spirals don’t totally match, and one is slightly incorrect, but you get the idea)
The thing that really amazes me about the Fibonacci sequence, however, is not the manner in which it can be used to create a cool looking spiral, but the frequency with which one can see this spiral in action. Look around you, it’s everywhere! Check out any nautilus shell, for example:
Or even look as far out as the depths of space towards this spiral galaxy (which, according to the source, make up 77% of our universe’s observed galaxies):
BUT WAIT, THERE’S MORE!
Ever heard of the Golden Ratio? If you went to art school, as I did, then you should already know all about it. However, most people did not go to art school, so I’ll give you a quick primer.
If the ratio of two numbers is the same as the ratio of their sum to the larger of the two numbers, then they are in the golden ratio.
This ratio has been used in art for centuries! Leonardo da Vinci believed that the proportions of human bodies were in the golden ratio. Other artists, such as Salvador Dali and Piet Mondrian, were known to utilize the golden ratio in their work. Salvador Dali even modeled the shape of his famous painting, the Sacrament of the Last Supper, in dimensions that conform to the golden ratio.
But what does the Golden Ratio have to do with the Fibonacci Sequence?
If you divide any number in the Fibonacci sequence by the number immediately preceding it in the sequence, the result is pretty damn close to the Golden Ratio.
You can see pretty plainly that this geometric interpretation of the Golden Ratio looks a LOT like some of the shapes created by the Fibonacci Spiral:
There is just SO MUCH to love about the Fibonacci sequence; I’ve just barely scratched the surface here! If you’re interested, a quick Google search will yield a tremendous amount of information on the subject. I couldn’t possibly recommend one resource over another because there is just so much out there!
Isn’t math so cool?