The Golden Mean

Golden mean in photography is a composition rule that states that an object should be placed at the intersecting points of two imaginary lines drawn according to the golden ratio. This rule is said to produce more visually appealing results and has been used by artists for centuries. The golden mean can be applied to any kind of photograph, but it is particularly well suited for portraits and landscapes. When composing a photograph using the golden mean, it is important to keep the horizon line in mind and to avoid placing the subject too close to the edges of the frame.

The Golden Mean has been a significant influence since ancient times, with Greeks employing the principle in their buildings such as the Parthenon on the Acropolis at the Temple of Athena. The Golden Mean was used for sculptures and paintings during the Renaissance period when European artists rediscovered ancient world styles. The Golden Ratio has been used in the visual arts by numerous well-known artists, including Leonardo da Vinci, who employed it in his masterpieces such as the Mona Lisa.

The Golden Mean, just like PI (3.14) is another of those strange numbers that we seldom question and very often take for granted. This number is represented by the Greek letter PHI, but dissimilar to PI, the golden mean goes very much unnoticed in our everyday life in such things as buildings, plants and even in living creatures - yet we find these things strangely pleasing on the eye. This is the magical number 1.618.

So how is this number found? An ancient mathematician by the name of Fibonacci discovered that if you start with the numbers 0 and 1 then add them together you get a new number - in this case 1. Easy enough but what if you add the last number and the new number together? You get another new number, 2(See figure below). Keep doing this and you will end up with a very very long list of unique numbers.

This is known as the Fibonacci Series - a sequence of numbers in which each number is the sum of the two previous numbers. The series was named after Leonardo Fibonacci, an Italian mathematician who first described it in the 13th century. Fibonacci numbers appear in nature, including in the arrangement of leaves on a stem and the spirals of a nautilus shell. Let's look closer.

0,1 --> add them together gives new number 1

0,1,1 --> add the last two number together and new number is now 2

0,1,1,2 --> add last two numbers together and new number is now 3

0,1,1,2,3 --> add last two numbers together and new number is now 5


The series eventually grows like below into a series of unique numbers

0,1,1,2,3,5,8,13,21,34,55,89,144, 233,377 to infinity and beyond!

So what do I hear you ask? Well, starting from zero and if you take any two SEQUENTIAL numbers and calculate the ratio between them then a very interesting pattern emerges below.

1,0  Ratio = 1 to 0 = 0

1,1  Ratio = 1 to 1 = 1

2,1  Ratio = 2 to 1 = 2

3,2  Ratio = 3 to 2 = 1.5

5,3   Ratio = 5 to 3 = 1.6666

8,5  Ratio = 8 to 5 = 1.6

13,8   Ratio = 13 to 8 = 1.625

21,13   Ratio = 21 to13 = 1.61538

34,21   Ratio = 34 to 21 = 1.61538

55,34   Ratio = 55 to 34 = 1.61764

89,55   Ratio = 89 to 55 = 1.6181

144,89  Ratio = 144 to 89 = 1.6179

If you keep going you will see that the decimal figure will revolve around the magic number 1.618. OK, I here you ask, but what is the point? Well lets look at the example of how the golden mean occurs in nature. Take a look at the diagram below. Notice that it is made up solely of squares, yet the overall image is a rectangle. This rectangle, if you measure it, has a magic ratio of 1.618. Also if you look at the curved lines within each of the squares you will notice that these are in fact quarter circles, but, as a whole you would be forgiven for thinking that they look like the cross section of a seashell.

And you'd be right, for this is the same as the growth rate of the beautiful Nautilus Sea Shell - i.e. 1.618.

Another interesting phenomena of nature is the sunflower. If you count the spirals you will see that there are 55 with either 34 or 89 on either side going in an anti-clockwise direction. Check it and see.

by Jeremy Merrifield

The Mean Screen

The golden mean can obviously be of huge benefit to designers when presenting new treatments to your clients. As we all know the client is always right and we have to go with their final say although sometimes we'd all like to think that they would accept some of our more illustrious designs.

As any film or television lover knows, the aspect ratio is the width to height ratio of the frame. The most common ratios are 4:3 (traditional standard definition TVs) and 16:9 (widescreen high definition TVs). However, there is a third option that is gaining popularity, particularly among those who appreciate a more cinematic experience: the golden mean.

However, when discussing an experiment to obtain the most pleasing size of TV screen the scientists made a number of various rectangular shaped TV screens with differing ratios and asked a large sample of people to state the best looking TV. The results were staggering and almost all of them preferred the TV with the ratio of 1.618. Now, it is becoming increasingly popular in the filmmaking world. Many directors are choosing to shoot their films in this format, as it allows for a more immersive experience. Additionally, many televisions are now being manufactured with this ratio in mind.

While the rule of thirds can be a helpful compositional tool, it also has its drawbacks. One downside is that following the rule too rigidly can result in predictable and lackluster images. Another potential problem is that the eye is naturally drawn to intersections, which can create an imbalance in the photo if not handled carefully.