It’s amazing how often one finds various mathematical concepts and postulations represented in nature and natural phenomena.

The Fibonacci Sequence

The Fibonacci sequence, is a sequence of numbers where each successive number is the sum of the previous two numbers, and the first two terms in thesequence are 0 and 1. It starts like this:

The fibonacci sequence generates spirals like this one:

I obtained an image of our galaxy, The Milky Way, and overlaid a few Fibonacci spirals on top of the spiral arms of the Milky Way. In spite of my horrible editing skills, the results were pretty fascinating:

Pretty amazing, right? The spiral arms of the galaxy coincide almost exactly with the spirals formed by the Fibonacci sequence. A bit more on this, including other pictures showing the relation between spiral galaxies and the Fibonacci sequence can be found here.

Fibonacci spirals are also found in sea shells. Observe how the shape of the following sea shell shows a striking resemblance to a Fibonacci spiral:

Even pine cones seem to have a certain affiliation with Fibonacci spirals…

The Catenary Curve

Dr. James Grime (from Numberphile and SingingBanana), made a video about the relation between the Catenary curve and where it can found in real life:

The Batman Equation

There’s this awesome equation which, when graphed, draws the Batman logo. Pretty interesting.

I’m not really sure where it came from, but according to some websites on the internet, it was made by some high-school teacher. Here’s a video about it too, from Numberphile:

Pascal’s Triangle

Pascal’s triangle has a lot of interesting patterns. I tweeted one of them a while ago…

Ever notice how one can get the 4 initial rows of Pascal's △ by repeatedly multiplying 1.1 by itself: 1.1, 1.21, 1.331 and 1.4641 ? #fb