Math on science (I)

Ever wondered how much influence math has in our everyday life?

It is not too much to say that almost EVERYTHING surrounding us is related to math, from the most obvious (engineering, statistics, computers etc) to less intuitive areas such as music and even biology.

As Galileo Galilei said in 1623: "The book of nature is written in the language of mathematics".

I'm sure all of you have heard the name Leonardo Da Vinci, some his contributions to so many areas in science, arts etc. are world famous, but maybe the name Leonardo De Pisa is not so well known. At least by his first name but, what about Fibonacci?

Fibonacci

Leonardo Pisano (1170 -1250) was a merchant and mathematician who lived in Italy and became known for spreading the hindu-arabic numeration system in Europe through his book Liber Abaci (Book of Calculation). In this book, as a solution for the problem of how the population of rabbits grows, it was written for the first time the sequence of numbers now known as Fibonacci Numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34...

Notice any pattern? In Fibonacci's Sequence you get every number by adding the two previous ones.

It may seem that there is nothing else to this sequence than meets the eye, and in fact it would have been like that if biologists and other scientists hadn't found some interesting properties.

The way that the shell of snails grow can relates to the fibonacci sequence in the way you can see in the following picture:

 As you can see, the side of each square is a number of the sequence.
There is also an interesting relation between these numbers and the way plants grow. Plants try to be as efficient as possible when absorbing light from the Sun, son no leaf is over another one. Usually branches in plants form a spiral around the stem. If you take the leaf at the bottom of the stem and count it as 0, and then you count all the leaves from there to the top, for most plants you will get a number of the Fibonacci sequence. Also if you count the laps that took you to get to the top (upwards spiral) it will also be a term of the sequence.
The way seeds are arranged in daisies and pine cones also form spirals that go around a number of times that is a Fibonacci number. If you count the petals in each layer in roses, you will alaso notice something...

Also the phalanxes in your fingers follow this rule. You have to admit there is a lot to this sequence....but there's more...
In a bigger scale, the arms of the spirals that galaxies form, are also arranged according to Fibonnaci's numbers.

But the last property I want to talk about today is one that will deserve a post on its own in the future: The Golden Ratio.

The golden ratio is an irrational number represented by the greek letter phi (φ or Φ = 1.6180339...), and it has been around for thousands of years. For artists and architects, it's a proportion that represents beauty. There  is a lot to say regarding the golden proportion, but as I mentioned before, we'll do that in the future. For now I want to talk to you about the relationship between this number and Fibonacci. As it turns out, if you divide any term of the sequence by its predecessor, the further you go into the sequence, the closer you will get to the golden ratio.

It is certainly curious that this sequence has so many properties, there are obviously more that the ones I mentioned, some of them related to advanced math, but I find it amazing that when Fibonacci thought of it, he had no idea of all it would mean...