One of the most long established rules within photography has been the rule of thirds. According to George Field in his book “Chromatics; or, The analogy, harmony, and philosophy of colours” (1845) the rule of thirds appears as early as 1797 as a rule for proportioning scenic paintings. The theory behind this rule of composition is encapsulated around balance. If you place points of interest along lines or intersections within a photograph, the overall effect will be more aesthetically pleasing.
The rule of thirds is used by many photographers as a simple method of achieving a athletically pleasing composition. A more technical and accurate method of creating an aesthetically pleasing image would be to use the Golden Ratio (spiral). This takes what is known as the ‘Fibonacci Numbers’ (0, 1, 1, 2, 3, 5, 8, 13, 21 etc) and applies them within the real world with the use of the golden spiral.
To explain this in more detail, I’ve placed a grid with the Fibonacci series of numbers within it. As you can see, it starts with 1+1 which is 2, 1+2 = 3 and so on. Fairly simple you may think. This next bit is when things start to get clever. Take, for example, boxes 5 and 8. You might think the difference between those boxes is pretty elementary, just another 3 boxes on each side. However, the length of the side of the 8 square divided by that of the 5 square is the (1.6180) golden ratio. So line B is x1.6 longer than line A. This sequence follows suit as the Fibonacci numbers increase.
This video below explains how the golden ratio works in a wonderfully visual way: