in which such parts are combined or related.
Composition is a very individual choice and has been the subject of debate for many
hundreds of years. When photography was first as in its infancy, it looked to the history of
the arts for inspiration in composition. There they found the rules that had been used for
many years before photography. Using these classic rules, photography developed its own
style and technique, but the basis rules of composition remain and are still widely used today
With regards composition, one of the great street photographers, Henri Cartier-Bresson,
wrote in his book:
“A photographer can bring coincidence of line simply by moving his head a fraction of a
millimeter. He can modify perspectives by a slight bending of the knees. By placing the
camera closer to or farther from the subject, he draws a detail…
and you’ll observe that, if the shutter was released at the decisive moment you have
instinctively fixed a geometric pattern without which the photograph would have been both
formless and lifeless.”
Henri Cartier-Bresson, 1908-2004. The Decisive Moment- 1952
The Fibonacci sequence and the Golden numbers
Leonardo of Pisa (Fibonacci) is considered the “greatest European mathematician of the
middle ages. He was responsible for many mathematical contributions. However, his greatest
contribution came from working out a puzzle about rabbits.
It was:
How Many Pairs of Rabbits Are Created by One Pair in One Year
A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know
how many are created from the pair in one year when it is the nature of them in a single month to
bear another pair, and in the second month those born to bear also.
He then went on to solve and explained the solution:
Because the above written pair in the first month bore, you will double it; there will be two pairs in one month.
One of these, namely the first, bears in the second month, and thus there are in the second month 3 pairs;
of these in one month two are pregnant and in the third month 2 pairs of rabbits are born, and thus there
are 5 pairs in the month; ...there will be 144 pairs in this [the tenth] month; to these are added again the 89 pairs
that are born in the eleventh month; there will be 233 pairs in this month. To these are still added the 144 pairs
that are born in the last month; there will be 377 pairs, and this many pairs are produced from the abovewritten
pair in the mentioned place at the end of the one year. You can indeed see in the margin how we operated, namely
that we added the first number to the second, namely the 1 to the 2, and the second to the third, and the third to the
fourth and the fourth to the fifth, and thus one after another until we added the tenth to the eleventh, namely
the 144 to the 233, and we had the above written sum of rabbits, namely 377, and thus you can in order find it
for an unending number of months.
From this we get the number sequence of:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…
Basics of Fibonacci sequence: Add the last two numbers to get the next.
The Golden Number
There is a ratio in nature that repeats itself. This number is referred to as the golden number,
golden mean or divine number.
It is a number runs to infinity and is called PHI- 1.618…
The inverse number is phi - 0.618…
At least since the Renaissance, many artists and architects have proportioned their works to
approximate the golden ratio; especially in the form of the golden rectangle, in which the ratio
of the longer side to the shorter is the golden ratio, believing this proportion to be aesthetically
pleasing. Mathematicians have studied the golden ratio because of its unique and interesting
properties.
The golden number repeats itself in nature over and over again. IN the curl of a sheep’s horns, the
human body, flowers, petals, trees, almost all nature has the proportions of the golden mean in their
make up.
The relationship between the golden number and the Fibonacci sequence is that if you divide the
each number by its neighbour, you get to the result of PHI, or the golden number:
Fibonacci sequence: …13, 21, 34, 55, 89, 144, 233, 377…
144 / 89 = 1.6179775…
89 / 144 = 0.6180556…
So it is seen that the Fibonacci sequence has a strong link to the golden mean. Along with the
golden number, we also see the Fibonacci numbers repeated in nature very often. These are not an
absolute, but the numbers are often repeated on flower petals, antlers on deer, leaves from a whorl
etc
Our eyes, from the day we are born, see the Fibonacci sequence and the golden mean in every day
subjects. These compositions are ingrained in our minds and we thus accept them as pleasing to the
eye. They form natural compositions and are our ingrained reference when we look at a picture,
look at art or take a picture.
"There is a close association in mathematics between beauty and truth"
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