The Golden Ratio in Nature

Although the Italian mathematician Leonardo Fibonacci introduced the numbers 0 to 9 to Europe, what he is best remembered for is a different series of numbers. Beginning with 1, the series is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55......  Known as the Fibonacci sequence, this string of numbers is generated by adding the previous two numbers in the list together to form the next. 

So what is the relationship to Fibonacci and the Golden Ratio? Divide any number in the Fibonacci sequence by the number before it, example, 55/34, or 21/13, and the answer is always a close approximation to 1.61803, this, the Golden Ratio.  Obviously, this is the reason that the Fibonacci sequence is sometimes known as the Golden Sequence.

As unlikely though it might seem, this string of numbers has a hidden beauty, a spiral that is the common denominator linking rabbits, cauliflowers and snails. Count the number of florets spiralling out from the centre of a cauliflower, and one sees two spirals running in opposite directions. The number of florets in each will be two consecutive Fibonacci numbers. For a great website, visit http://www.math.smith.edu/phyllo//

In 2003, scientific findings revealed that the shape of the Universe is a Dodecahedron, this form based on Phi. Remarkably, it was Socrates who first suggested that this is the form of our universe. The story of this accounting is told in Plato’s Tenth Republic when after drinking the hemlock, Socrates who was thought dead, suddenly awoke and spoke to his grieving disciples. What did he tell the before laying back down to die? That the Universe was shaped like a child’s soccer ball. And yes, even then, a soccer ball was based on a dodecahedron. 

To bring the Golden Ratio a bit closer to home, it is interesting to know that the dimensions of the Earth and that Moon have a Phi relationship in that they form a Golden Triangle. This is the same geometric construction that some believe was used in the construction of the Great Pyramid of Egypt. Many species of plants and trees are covered in leaves. Their arrangement is not random, and neither leaves nor flowers emerge by chance. The point where every branch and leaf emerges does so based on fixed laws and extraordinary measures.  Plants are ‘Golden’, having obeyed the law of the Golden ratio since their creation.

To make this ratio personal, DNA is based on the golden ratio, for Nature tasks two golden spirals with storing all information regarding the physical features of every living thing. The ratio is found in DNA’s two intertwined perpendicular helixes. The length of the curve of one helix 34 angstroms, and the width 21 angstroms, 21 and 34 being sequential Fibonacci numbers. 

In 2010, Science Daily reported that the Golden Ratio has been discovered in the quantum world, this hidden symmetry observed for the first time in solid State Matter.