WARNING: A VERY LONG POST
It doesn't quite matter whether if it makes any sense now, soon it will. Hopefully.
As I went through further with this Golden Ratio business, I learnt that it's not only related to maths (Fibonacci sequence, pi, irrational numbers) and arts (divine proportions, davinci) - the only ones I know of, it touches on so much more: biology, music, structure and ofcourse, architecture; also recently what I believe photography should be included =P
Following wiki, I'll break it down into 3 main topics - aesthetics, nature and maths.
1 Aesthetics being the most related to topic, Da Vinci worked on the Vitruvian system of rational proportions and the Divine
Proportions - and how this all linked up from harmonious proportions and more importantly pleasing compositions, to our body's natural proportions in nature's creation. The first link builds between Art and Maths. Though unofficial, it's been claimed DaVinci painted MonaLisa within the scope of the Golden Ratio and at the same time,Pablo Tosto (researcher) listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and root-5 proportions, and others with proportions like root-2, 3, 4, and 6. The point I'm trying to make here isn't the absolute formula which rules the universe but the similarities which draw these different line of topics together under the same law, all working out in their own way.
2 [Complete copy off wiki] Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these phenomena he saw the golden ratio operating as a universal law. In connection with his scheme for golden-ratio-based human body proportions, Zeising wrote in 1854 of a universal law "in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form"
3 Maths; well all there is to it is the understanding of the Golden ratio, and I choose not to further the discussion into it because it doesn't directly link back to aesthetics. Though we have to keep in mind the things to remember are:
- it almost looks like a 2:1 ratio between a+b
- simplified to closest rationals, b = 1/3 (0.333..)
- actual ratio is 1:1.61803...
- a can be also otherwise substituted with 1.61803 (phi), and b as 1
ULTIMATELY the link,
After all the hustle and bustle of name droppings and formula shoving, one thing remains constant - everyone's relation to the golden ratio is unavoidable. The idea is that the proportions, to its approximate, surges a connection through our visual appreciation metaphysically, to naturally be prone to accept such a composition - while at the same time in it's exact numbers, serves a higher purpose of patterns and systematic pragmatics - in maths, structures, rhythm & music.
I will also not dwell into architecture examples, as I believe it's not hard to study up on Greeks Acropolis, NotreDame, LeCorbusier and MarioBotta's works (all of which quite prominent with relations to the Golden ratio - all serving for harmonious proportions altogether) "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned." Le Corbusier
As they say,
Practice makes perfect, and
Trial and error gets you one step closer.
As the world act in it's nature of survival and progress
Each individual finds and eventual stage of comfort and solution.
The Law of survival (of the fittest) passes the bests
and the bests make a point.
Linked together across the world, the points make a connection
A connection generates a similarity, and
Similarities generate a pattern.
Patterns make proof,
Proof makes evidence, and
Evidence make inevitability.
Thus the creation of the system of our universe.
The cheat here, (at least for us visual impress-ors) is to easily manipulate your visuals (in composition and proportions) to follow the golden proportions, even slightly, it makes an impact.
E.g. Photographers have been told to follow a rule - The rule of thirds (where your main subject only fills up 2/3 of the frame) - which generally aimed for novices, it teaches them the first steps of composition to create a "nice picture"; looked closer, its 0.66.. much like the proportions of a/a+b (above) = 0.618...
Other examples such as Music, listed, is adherent in terms of structure and rhythm - not entirely related but visible. Further studies could go into Pi, Fibonacci, Da Vinci, and so on, but I warn you. People dedicate their whole lives to the study of the Golden Proportions because of its divinity - I merely want to extract the cheat code here of visual appreciation to create an upper hand in design and effective proportion compositions.
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