A great while back I started reading The Golden Ratio, a story of PHI, a never ending, digits never repeating number ~ (1.61803398…..). In a previous post, I was just getting through the introductory chapters and was excited to read more about how phi shows up all over nature. Well, it’s taken me a while for many reasons – time constraints, my exceptionally poor and slow reading skills, the ruler that I was using to read line by line broke and it took my 5 weeks to find some scotch tape to fix it … but I have finally got to some very interesting parts of the book. My appetite for the mind boggling ways this ratio appears everywhere is slowly being fed.
The Fibonacci Sequence, as seen in The Davinci Code, has shown up a lot – a sequence of numbers where the prior two add up to the next, so 1 1 2 3 5 8 …, and so on. It turns out that the higher the Fibonacci sequence goes, when you look a the ratio between two consecutive numbers in the sequence, it converges to PHI – the golden number. You can see this pattern here:
5/3 = 1.667
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615
And when you think of a Fibonacci sequence as a rate of growth, and apply this to nature, the golden ratio shows up many places. The arrangement of floret in the head of a sunflower, the placement of leaves on a stem, the hexagonal scales on the surface of a pineapple, and the beautiful nautilus shell all have the golden ratio incorporated into their structure. The nautilus shell, has the unique property that as it increases in size, it’s shape remains unaltered – "although changed I rise again the same" – Jacques Bernoulli (1654-1705).
Beyond structural patterns, I was fascinated to read about the flight pattern of the Peregrine falcon and how they follow a logarithmic spiral (resembles the nautilus shell) at speeds of over 200mph when attacking their prey! And this one is really crazy … mapping the family tree of a drone bee. A drone bee you ask? This is a male bee who hatched from an unfertilized egg. An unfertilized egg you ask? I have no idea … so please don’t ask! These drone bees have no father and one mother. Female bees, on the other hand, are born from the fertilized queen’s eggs and become female workers or queens themselves. The book then outlines the intriguing family tree of a drone bee:
one drone has one parent (its mother), two grandparents (its mother’s parents), three great-grandparents (two parents of its grandmother and one if its grandfather), five great-great-grandparents (two for each great-grandmother and one for its great-grandfather), and so on. The numbers in the family tree1, 1, 2, 3, 5 … , form a Fibonacci sequence.
There is so much beauty in these numbers – they are what makes nature so exquisite. I am now half way through the book, and have officially added it to my recommendation list! Here’s hopping the end of the book is less than 6 weeks away!!!