# What Exactly is "1:1.618" ?

### #1

Posted 04 September 2011 - 04:49 AM

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

### #2

Posted 04 September 2011 - 05:15 AM

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

Wikipedia Article

### #3

Posted 04 September 2011 - 05:24 AM

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

http://en.wikipedia....ki/Golden_ratio

http://en.wikipedia....th_golden_ratio

### #4

Posted 04 September 2011 - 05:46 AM

### #5

Posted 04 September 2011 - 07:19 AM

### #6

Posted 04 September 2011 - 09:23 AM

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.

### #7

Posted 04 September 2011 - 10:15 AM

### #8

Posted 23 September 2011 - 10:28 AM

### #9

Posted 23 September 2011 - 07:29 PM

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.

### #10

Posted 23 September 2011 - 07:47 PM

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 by Chris Millar, 23 September 2011 - 07:48 PM.**