To someone who genuinely would like to know and doesn't have a clue, your answer is not of much help I'm afraid I'm a great fan of google, but even so, it's not as though the answer jumps out at you.
A formula without a context makes no sense at alllol, maybe... you are right, the answer does not jump out on google, it takes hours and hours of searching. Which is what i have done and pieces together this:
LOL, maybe you are right, the answer does not jump out on google (well unless you type golden ratio planted tank, that takes you directly to the APC article!!), it takes hours and hours of searching. Which is what i have done and put together this in the last few days.
I would call it part 1, if i had time to make a part 2. I need to reference some areas which i have taken directly from books and websites.
------------------------Golden Ratio, Part 1 ---------------------------------
What is the golden ratio?
The first recorded use of the term golden ratio is thought to be by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The words he used directly translated from German means "golden section".
The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. However, the practical use of the golden ratio was used much longer ago, even dating back to the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). Even in a recent science fiction novel, the character Robert Langdon in the “Da Vinci Code†makes a connection of the golden ratio to the historic pentagram and Fibonacci sequence.
Although we will briefly cover the math which denotes the formation of the golden ratio, the true theoretical understanding involves complex mathematical calculations. Due to the deep and limited need for this understanding, we shall steer away from this route and delve deeper into its practical implications and use in the aquarium.
The golden ratio is often represented by the Greek letter, phi, φ and in fact represents a irrational number. This number is often stated as 1.6180 (as erroneously labored on in the Da Vinci Code) however strictly speaking, this is not exactly true since the number is being rounded an approximation and can never be an exact quantity. We are now being far to precise, since our need for the golden ratio is well suited to this erroneous approximation and for our understanding and the remainder of this article we shall name it as that, 1.618.
So what is so special about the number and how can it be used in the aquarium? The number is also regularly referred to by artists as the divine number and it is the division of a given unit of length into two parts such that the ratio of the shorter to the longer equals the ratio of the longer part to the whole.
In more simple terms, it gives us a guide to the aesthetic positioning of décor in the aquarium. Let us take for example a simple tank in which we want to place one lone rock, where would we naturally place it? I doubt it if many of you would place it perfectly central in the tank, most of us would naturally place it just off center to disturb the symmetry for more relaxing feel.
..............and thats as far as a got!
Hope that was useful, i will going to explain how it is used in the aquarium but to be honest the APC article is OK.
The best way of working out how it is used is by copying some Amano tanks and adding the grid lines, i have done this to loads of tanks and my understanding really developed this way!
I do not make fantastic tanks, i do not propose to know it all, but i have done my research and this takes time and effort so maybe people should be a little more persistant with their searches. I often come on the net at 7pm after work and chat to other hobbiests on msn and read the forums literally until 1-2am....nearly every night!
Anyway, thats besides the point. Hope this time you found my post helpfull, Bloo ?
Regards
Chris