Phi…

Dear Editor,

Phi (φ) is the most amazing number in the universe. Phi = (1+√5) ÷ 2 which equals 1.6180339… and is commonly known as the golden ratio, the golden mean or golden section. Phi (φ) is also known by other names including: divine proportion, divine section, golden proportion, golden cut, and golden number. Like pi (π), phi knows no end to the right of the decimal point.

Phi is the only number that when you add 1 to it, you get its square (2.6180339…) and when you subtract 1 you have its reciprocal (.6180339…). Try this on your calculator.

Nearly all of creation is constructed on this ratio.

“Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient 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 and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. 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

The Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, …. is an approximation of the golden ratio when dividing one of the numbers in the sequence with the previous number. As the numbers get larger the closer we get to the actual golden ratio number.

There are several geometrical methods for the defining of the golden ratio which is described in detail on the internet.

In ancient architecture structures, such as the Parthenon, the Great Mosque of Kairouan and the Great Pyramid, were constructed using the golden ratio.

Artists Leonardo da Vinci, Salvador Dalí and Piet Mondrian used the golden ratio in their paintings.

Composers Béla Bartók, Erik Satie and Debussy have incorporated the golden ratio in their works.

There is so much more I could have written about phi (φ), but since my articles have been banned from the Reader, I can only submit letters that are constrained by a 400 word limit.

“The Universe is nothing but the Divine uttering its own name to itself.” –Ramakrishna

Lee Santa
Sandpoint