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The Golden Mean 


I have
always been fascinated by ancient mathematical rules and how they
have been applied in design. The "golden rectangle" or "golden mean"
is one such rule if you like, that has often sneaked its way into my
design work  sometimes planned but more often than not it just
seems to happen.
Let me explain. The Golden Mean, just like
PI (3.14) is another of those strange numbers that we seldom
question and very often take for granted. This number is represented
by the Greek letter PHI, but dissimilar to PI, the golden mean goes
very much unnoticed in our everyday life in such things as
buildings, plants and even in living creatures  yet we find these
things strangely pleasing on the eye. This is the magical number
1.618.
So how is this number found? An ancient mathematician
by the name of Fibonacci discovered that if you start with the
numbers 0 and 1 then add them together you get a new number  in
this case 1. Easy enough but what if you add the last number and the
new number together? You get another new number, 2(See figure
below). Keep doing this and you will end up with a very very long
list of unique numbers.
This is known as the Fibonacci
Series.
0,1 > add them together gives new number 1 0,1,1
> add the last two number together and new number is now
2 0,1,1,2 > add last two numbers together and new
number is now 3 0,1,1,2,3 > add last two numbers
together and new number is now 5 0,1,1,2,3,5
The series eventually grows like below into a series of
unique numbers
0,1,1,2,3,5,8,13,21,34,55,89,144, 233,377 to infinity and
beyond!  So what I hear you ask?
Well, starting from zero and if you take any two SEQUENTIAL numbers
and calculate the ratio between them then a very interesting pattern
emerges below.
1,0 Ratio = 1 to 0 = 0 1,1
Ratio = 1 to 1 = 1 2,1 Ratio = 2 to
1 = 2 3,2 Ratio = 3 to 2 =
1.5 5,3 Ratio = 5 to 3 = 1.6666 8,5
Ratio = 8 to 5 =
1.6 13,8 Ratio = 13 to 8 =
1.625 21,13 Ratio = 21 to13 =
1.61538 34,21 Ratio = 34 to 21 = 1.61538
55,34 Ratio = 55 to 34 =
1.61764 89,55 Ratio = 89 to 55 =
1.6181 144,89 Ratio = 144 to 89 =
1.6179  If you keep going you will see
that the decimal figure will revolve around the magic number 1.618.
OK, I here you ask, but what is the point? Well lets look at the
example of how the golden mean occurs in nature. Take a look at the
diagram below. Notice that it is made up solely of squares, yet the
overall image is a rectangle. This rectangle, if you measure it, has
the magic ratio of 1.618. Also if you look at the curved lines
within each of the squares you will notice that these are infact
quarter circles, but, as a whole you would be forgiven for thinking
that they look like the cross section of a sea shell. And you'd
be right, for this is the same as the growth rate of the beautiful
Nautilus Sea Shell  i.e. 1.618.
Another interesting phenomena of nature is the
sunflower. If you count the spirals you will see that there are 55
with either 34 or 89 on either side going in an anticlockwise
direction.Check it and see.
(Photo 
Jeremy Merrifield at http://stock.d2.hu/)
The Mean
Screen.
The golden mean can obviously be of huge benefit
to designers when presenting new treatments to your clients. As we
all know the client is always right and we have to go with their
final say although sometimes we'd all like to think that they would
accept some of our more illustrious designs.
Consider
however, the following...Whilst I was was watching TV a few years
ago (I can't remember the programme but I do remember the subject),
they were discussing an experiment to obtain the most pleasing size
of TV screen. They made a number of various rectangular shaped TV
screens with differing ratios and asked a large sample of people to
state the best looking TV. The results were staggering and almost
all of them preferred the TV with the ratio of 1.618.
About
a year ago, I bought a wide screen TV so I measured this and it has
a viewing area with a ratio of 1.618  check yours for size.
Remembering the TV programme I thought I would put some design
treatments to the test with my clients. I presented half of them
with what they wanted and the other half with designs conforming to
some form of the golden rectangle ratio. Each of the designs
conforming to the ratio was accepted almost straight away and the
client was pleased with the results.The others, well you know the
story, 'can you change this', ' I don't like that' etc., etc. I
thought there must be something in this so I reintroduced some of my
less mainstream designs to clients who had rejected them but tweaked
them to have ratios around the golden mean and some of them were
preferred to the existing design. Yes the samples were small but
weird stuff indeed.Whilst, I am not saying that this is the be all
and end all of design, I am saying that it is worth giving a try.
You never know, it may just save you time and effort.






















 





Published with the permission of the author.

