(NOTE: For the sake of focusing on the practical aspect of this information, I have omitted most historic information in this draft)
The Math of Art: Fibonacci Numbers Vs the Rule of Thirds
Fibonacci Numbers is the term given for numbers of a specific sequence. This sequence begins with the numbers 0 and 1. In this sequence,
by adding the preceding two numbers, we derive the next Fibonacci number. The sequence, therefore, is as follows:
0,1,1,2,3,5,8,13,21,34,55,89...
continuing indefinitely.
Fibonacci numbers are a valuable asset to the artist due to their association with The Golden Ratio,or Phi. Any two Fibonacci numbers, in order, starting from 55:89 approximates Phi, or the ratio 1:1.618. The smaller of the two numbers is referred to as the golden section of the longer. This ratio is also called The Divine Ratio, owing to it existing in numerous natural forms. This ratio may be found frequently in the relative distances within the human form. Phi may be found in the features of the face, and length of arms, and legs. The entire body itself is also divisible by said ratio.
To the Artist, this means that by using Fibonacci numbers and golden sections instead of the more popular approximation of thirds, one can accurately measure the human form instead of relying on shorthand. An artist may ask, Why? Artists have been using the rule of thirds for generation, so why abandon an established tradition in favor of measuring in Fibonacci numbers? The answer is twofold. Firstly, we must understand the reason why the rule of thirds is used; secondly, we must address that the methods produce different results.
The rule of thirds is an easier method. Thirds are easier to approximate with the eye than Phi. To an artist, even with Fibonacci numbers, using units of 1,2,3, is far more approachable than 55,89,144, etc.. For most learning artists, using such units to draft without extra tools or an extraordinary affinity for numbers would have been extremely difficult in the past; however, The modern artist must understand that the medium has changed, and the popularity of digital mediums and the pixel as a unit of measurement makes utilizing larger numbers much easier . The artist can also use Phi when working in physical mediums, as printing a guide created by measuring pixels and scaling them to fit ones desired size.
If both may be used, why choose the more complex method? Accuracy. Above, I refer to the rule of thirds as the "approximation of thirds". This is because, realistically, thirds is just that, close, but not the same. Simply put, The rule of thirds is inaccurate. The ratio of thirds, when measuring the same distance actually representable by Phi, uses the following ratio:
3:2
or
1.66:1
as opposed to Phi:
1.618:1.
This difference of .042, when applied to the human body, can cause significant distortions. The chin and nose elongated, or horse-face, as some would call it, being a common result.
