

Oskar Barnack (18791936)
"In the first
years of the art, photographers were mainly concerned
with hauling their heavy plate cameras from one location
to the next. Their trials and tribulations stimulated
Oskar Barnack into seeking a completely new method of
taking photographs.
Even as early as
1905, he had the idea of reducing the format of negatives
and then enlarging the photographs after they had been
exposed. It was ten years later, as development manager
at Leica, that he was able to put his theory into practice.
He took an instrument for taking exposure samples for
cinema film and turned it into the world's first 35 mm
camera: the 'UrLeica'.
At the time, the miniature film format of 24 x 36 mm was
created by simply doubling the cinema film format. The
first photos  of outstanding quality for the time  were
made in 1914. Progress was interrupted by the First World
War, so the first LEICA (Leitz Camera) did not go into
serial production until 1924, being presented to the public
in 1925."





Oskar Barnack and the 3:2 Aspect Ratio
The origins of the aspect ratio of 35mm film can be traced
to Oskar Barnack, an employee of Leitz Camera in Germany. Barnack
believed the 3:2 aspect ratio to be the ideal choice for his
invention, the first 35mm camera ever, dubbed the "UrLeica".
After WWI, Barnack convinced his boss, Ernest Leitz II, to begin
production of similar cameras. In 1925, Leitz Camera released
the first Leica and the rest is history. Why was Oskar Barnack
so adamant about the seemingly arbitrary aspect ratio of 3:2?
There are many other film formats with different aspect ratios
to choose from, but there is something special about the 3:2
aspect ratioit happens to have the closest proportions to
the Golden Rectangle of any other major film format out there,
with the sole exception of European widescreen. Perhaps Oskar
Barnack had this in mind when he created the 3:2 aspect ratio.
What Is the Golden Rectangle?
The Golden Rectangle is defined as a rectangle that can be
partioned into a square and a smaller rectangle which has the
same aspect ratio of the original rectangle. In Figure 1, we
see such a rectangle. In this example, the length of the smaller
rectangle divided by its width is equal to the length of the
larger rectangle divided by its width, i.e., a ÷ b =
(a + b) ÷ a. The ratio of the larger side of each rectangle
to the smaller side is known as the Golden Ratio. Mathematically,
this works out to be about 1.6:1, or 3.2:2 compared to the 3:2
aspect ratio of 35mm film.
Figure 1: The Golden Rectangle.
The Golden Rectangle in Nature
The Golden Rectangle and Golden Ratio appear in some very interesting
places. For example, in Fibonacci numbers, a sequence of numbers
where each new number is the sum of the previous two numbers
(1, 1, 2, 3, 5, 8, 13 . . .), the ratio of consecutive numbers
increasingly approaches the Golden Ratio. In Figure 2, we see
a graphical relationship between Fibonacci numbers and the Golden
Rectangle. The Fibonacci numbers are closely related to exponential
growth, such as the reproduction of rabbits. They are also found
in plants where many tend to have a Fibonacci number of petals
or leaves.
Figure 2: Relationship between the Fibonacci
sequence and the Golden Rectangle
Another interesting place the Golden Rectangle
appears is in spirals. Successive points dividing a golden rectangle
into squares lie on a logarithmic spiral, also known as the
"Spira Mirabilis". See Figure 3. Coincidentally, spirals
such as these are found throughout nature, such as in the contours
of Nautilus shells.
Figure 3: The Golden Rectangle and Spira
Mirabilis
The Golden Rectangle in Art
The Golden Rectangle is believed to have been first constructed
by Pythagorus in the 6th Century B.C. It is said to be one of
the most visually pleasing of all geometric forms. Archeologists
have found countless examples of it in the facades of ancient
Greek architecture. In Figure 4, we see how the Parthenon in
Athens was built to the dimensions of the Golden Rectangle.
Figure 4: The Parthenon
In Figure 5, we also see how Leonardo da Vinci
applied the Golden Rectangle to the proportions of the human
body. In this example, the height of the person was divided
into two segments, the dividing point being the person's navel.
Leonardo took the distance from the soles of the feet to the
navel, then divided by the distance from the navel to the top
of the head and found that it was equal to the Golden Mean,
or as he would call it, the Divine Proportion.
Figure 5: Leonardo da Vinci's study of
the human body
The Golden Rectangle also has its place in modern
art such as in the paintings of Piet Mondrian. In Figure 6,
we see one such painting.
Figure 6: Piet Mondrian, Composition
in Red, Yellow, and Blue
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