Something mentioned frequently in the mathematical world is that the Fibonacci numbers often appear around nature. It is also in science, architecture, we even found it in literature.
Rather than explaining some applications, I thought I would show you a neat video I found instead.
I find all of the applications fascinating, as well as the fact that we can easily draw our own golden rectangle. You don't even have to be an artist to do it.
Bonus: In the video, they mentioned that if you take the square out of the golden rectangle, the remaining rectangle is a golden rectangle. You can prove this 2 ways.
First off, the sides of a golden rectangle can be two consecutive Fibonacci numbers. Say they are 55 and 89.
If you cut off a 55x55 square, you are left with a 34x55 rectangle. Since these are two consecutive Fibonacci numbers as well, it is a golden rectangle.
The more interesting one, however, is to look at the golden ratio itself. If you do 1/1.618034..., you get 0.618034...
In other words, phi:1 = 1:phi-1. So, if we cut off a 1x1 square from the rectangle with side ratio phi:1, we are left with a side ratio of 1:phi-1, which is the same as before. I found this really cool about Fibonacci numbers.