What Exactly is "1:1.618" ?

[manigandan srinivasan]

I had a class recently about "The Golden Mean" & "Rule of One thirds". i came across the "GOLDEN MEAN". i understood the rules on composition. But, i want to know The exact history of how it was found,what it means,how it works.

I did google abt it. But, it took me deep into maths. so i am expecting some clear,simple explanations about it .

[Hal Smith]

There isn't a "simple" explanation. It's a mathematical concept and requires math to solve it.

 

(1 + (sqrt)5) / 2 is as simple as it gets. Since (sqrt)5 is an irrational number, the Golden Mean is irrational.

 

Wikipedia Article

[Brian Drysdale]

With so much history with the maths crossing over into the arts I suspect there aren't any great simple explications other than it looks good and the ratio seems to be found in nature.

 

However, you could try these as a starting point and ignore the maths:

 

http://en.wikipedia.org/wiki/Golden_ratio

 

http://en.wikipedia.org/wiki/List_of_works_designed_with_golden_ratio

[manigandan srinivasan]

Thank you :).....

[manigandan srinivasan]

This documentary on "golden ratio" Might help us to understand it clearly from how it works :)

http://www.youtube.com/watch?v=qpAJ5mMHGwY

[Dom Jaeger]

It's probably the most interesting ratio there is (and there are some very interesting ones out there!)..

 

The easiest way to visualise it as a rectangle of sides 1 and 1.618 (or 0.618 and 1 - the ratio is the same).

 

It creates a very pleasing shape, but the magic comes when you divide it into a square and another rectangle. The smaller rectangle will have exactly the same proportion as the larger rectangle. Segment the smaller rectangle with a square again and you are left with an even smaller rectangle of the same proportion, ad infinitum.

 

You can do the same thing with a line, dividing it into a smaller and larger portion with the ratio 1:1.618 (or 0.618:1). The proportional relationship of whole line to large section is the same as that of large section to small section. There exists only one point in the division of a line into 2 unequal parts that creates this proportional symmetry - the golden section.

 

So it can be used not only as a framing shape, but also to divide linear space, or create more complex forms such as spirals.

 

In nature it creates patterns that remain the same proportionally no matter how big they become.

 

It also pops up in all sorts of seemingly unrelated mathematical areas from the Fibonacci series to tiling patterns.

 

I suspect we respond on some subconscious level to the proportional symmetry of the ratio and find it aesthetically pleasing.

[Brian Drysdale]

A quick BBC run at the ratio.

 

[Daryn Williams]

It basically is pleasing to look at... People noticed this, and tried to quantify beauty...

[Dom Jaeger]

It basically is pleasing to look at... People noticed this, and tried to quantify beauty...

 

No, it was a mathematical discovery first. It's a very specific ratio relating to growth and proportion, which was seen as mystical (rather than aesthetically pleasing) by early geometricians who were searching for mathematical answers to the universe. They incorporated it in their architecture and art, and through the centuries other artisans and artists with a mathematical interest have continued to find it inspiring. The aesthetic beauty derives from the various interpretations of its mathematical properties, not vice versa.

[Chris Millar]

Alan Turing - one of the grandfathers of computer science researched Fibonacci sequences in his work on Morphogenesis ... fascinating stuff.

 

I've got a copy of a book he read as a child 'Natural Wonders Every Child Should Know' - you can see obvious influence on his later interests in it.

Edited September 24, 2011 by Chris Millar