# Dividing the Frame-The Golden Section Proportions

I had read the section on Dividing the Frame in the Michael Freeman’s textbook previously, while looking at balance. The principle that geometric divisions of the frame would contribute to balance and harmony seemed logical, however, what the ‘harmonious’ division might look like was not obvious to me.

I read the ratio calculation formula and at first glance the calculation seemed understandable. As I read further, the maths began to overwhelm me and no matter how much I studied the photographic examples on page 27, the divisions were not clear. I decided to put it aside for another day.

On reading ahead in the course text to Frame Shapes and Sizes, I learned that the image taken inside the church corresponds closely to the ideals of the Golden Section. In what way, I asked myself. This prompted me to revisit the Freeman textbook in an attempt to enlighten myself.

On studying the text and examples of geometric and Fibonacci divisions the frame was divided into several areas which made me wonder, how can this work if the formula is only for 2 values?

I looked at the Golden Ration Frame section and revisited pages 40-43 on ratio and balance. I applied the 3:2 ratio (standard 35mm, now digital SLR frame) to the Golden Section Proportions formula,  a+b ⁄a   =    a⁄b , where the larger part is a. Resulting in the value of  φ = ½(1+5) = 1.618033989

3+2⁄3    =   which is 1.66666666667

3⁄2 = 1.5, whilst not exactly corresponding, I was encouraged enough to continue.

I considered the illustration on page 27 of the geometric divisions and after some time and calculations realised that I had been viewing it as 4 separate areas rather than 2 divisions of 3:2.

I decided to see how this division would look with one of my previously taken photographs. Although not conforming exactly to the Golden Section ratio, I think this 3/2 division works well for this image using the red line.

I next decided to look at the Fibonacci numbers, 1, 2, 3, 5, 8, 13, 21, 34, 55 … I realised that again I had not focused on applying pairs on numbers to the ratio. When I applied the numbers in ascending pairs to the Golden Section Formula I noticed that, although the early numbers didn’t marry with the 1.618033989 ratio, as they ascended they very quickly did so.

2/1 = 2.0

3/2 = 1.5

5/3 = 1.67

8/5 = 1.6

13/8 = 1.625

21/13 =1.615

34/21 =1.619

55/34 = 1.617

I thought it would be interesting to see how a few of these ratios could be applied to my photographs.

The photograph above was divided 5/3. I personally think this is a good division for this image on both planes. The blue line separates the 2 tallest towers from the others in the distance. The red line skims the top of the central tower. The intersection point of both lines is placed at the top of the central tower.

The division used above is 8/5. While the blue vertical line is not  good fit for this image, the red horizontal line separate the sea from the houses and sky.

Having worked through the textbook and exploring different divisions and ratios, I feel a lot more comfortable with geometric division of the frame.  Freeman stresses precision is not of the upmost importance, nor is there little need or opportunity for photographers to calculate exact ratios before composing a shot. However, I do think it is has been of value for me to understand that when a large and small section of the frame are integrally related by ratio, they are tied together thus providing a sense of harmony. Freeman suggests that if a photographer becomes familiar with which proportions are visually satisfying then their intuitive composition will become more finely tuned.