Some mathematical ratios appear to have mystical powers or, at the very least, hold the key to powerful relationships in nature and beyond. In 2002, Mario Livio, an Israeli-American physicist who works at the Space Telescope Science Institute, wrote a book called The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number. It’s all about a certain irrational number (a number that cannot be expressed as the ratio of two integers), namely 1.618 …, called phi (φ). This number, φ, denotes what ancient Greek mathematicians called the golden ratio, an instance in which the ratio of two quantities (a and b) is the same as the ratio their sum (a+b) to the larger of the two quantities.
Livio wrote:
Some of the greatest mathematical minds of all ages from Pythagoras and Euclid in Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
Mario Livio- physicist
Some of the greatest mathematical minds of all ages from Pythagoras and Euclid in Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
Check it out.
The golden ratio governs the number of petals in a flower, determines the spiral pattern in seed heads (just picture the center of a sunflower), governs the seed pod arrangement of pinecones, explains the way tree branches form or split, determines the structure of spiral shells (for example, the nautilus), perfectly describes the structure of spiral galaxies, applies quite accurately to the structure of hurricanes, explains the relationship of the features of the human face to one another, accounts for the fact that the length of each section of our fingers is larger than the preceding one by φ, describes the proportions of human and animal bodies, forms the flight pattern of birds of prey as spiral down on their targets, and describes the structure of the DNA molecule.
I can’t tell you why the golden ratio is golden, but I can tell you that, in its way, the Pareto Principle—the 80/20 ratio—is golden, too. Like the golden ratio, 80/20 applies to a dazzling array of disparate phenomena. The Italian polymath Vilfredo Pareto (1848-1923) discovered that 80 percent of the peapods in his garden were produced by just 20 percent of his pea plants and, conversely, just 20 percent of his pea plants produced 80 percent of his viable peapods. Then he discovered that in any system of almost any kind 20 percent of the input is responsible for 80 percent of the productive output, whereas the other 80 percent of the input is essentially wasted—non-productive. This applies to everything from labor and investment to profit. A business generates 80 percent of its profit margin from the combination of just 20 percent (its best customers) buying 20 percent of its products (which are therefore its best products). Look closely at yourself, and you will discover that 80 percent of what you achieve in a given workday is the product of 20 percent of your time. Great! But it also means that 80 percent your daily minutes and hours result in trivialities.
Successful CEOs and managers use 80/20 to design businesses that focus 80 percent of their resources on serving the 20 percent of customers who generate 80 percent of their profit. There is no intuition or guesswork involved in creating an artwork or a building according to the golden ratio. Likewise, harnessing 80/20 for profitable growth demands no creative genius. Whether you are applying the golden ratio or the Pareto Principle, you need only gather the data, work the numbers, and act on the result of this analysis. Best of all, you don’t need to understand why 80/20 works any more than you need to understand why the golden ratio so dominates our world. Both 80/20 and the golden ratio simply work. Take advantage of the gift, gather the data, work the numbers, act on the result, and enjoy your success.