Phi, The Golden Ratio

Maths has a bad reputation as a school subject. Probably the most common complaint uttered in a maths class is that “I’m never going to use any of this!” Almost everyone understands the vitality of basic arithmetic (addition, multiplication, etc..) but draw a line when confronted with algebra, trigonometry and calculus.

However, many people don’t realise that there is a number that appears everywhere in our daily lives. This number is present when you look at a portrait or a flower, listen to a song, even in DNA and astronomy!

And that number is PHI.

PHI (pronounced fie {like pie}) is the number , which is approximately 1.618, and is also known as the “Golden Ratio”. Phi is not pi (3.1416, the number plaguing students as they calculate the area of a circle), but a completely separate irrational number.

Phi can be derived through the Fibonacci series, a numerical series where each number is the sum of the two numbers prior to it (excluding the first two numbers in the series.)- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55….

This ratio is supposed to be the most aesthetically pleasing for a rectangular shape- i.e. if one side of a rectangle is 1 unit, the other should be 1.618. This ratio was used in the Pantheon in Greece due to these aesthetically pleasing properties. The Renaissance artists called it the Divine Proportion and used it for beauty and balance in designing their artwork. The ratio is also found in the Notre Dame in Paris.

Even music has a basis in the Fibonacci series, as there are 13 notes in the span of any note through its octave. A scale is composed of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords.

The dimensions of the Earth and Moon are in Phi relationship, forming a Triangle based on 1.618. Many flowers have petals that total a number in the Fibonacci series: Lilies have 3 petals, buttercups and roses have 5, marigolds have 13 and daisies have 55 or 89.

The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.

This number, phi, and its relative, the Fibonacci series, provide the very building blocks of the environment around us. No one knows why this mysterious number appears so frequently, but it is an example of how numbers form the foundation of the world we live in.


Article by Aoife Kearins