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    35mm Film and the Golden Rectangle
 

Oskar Barnack (1879-1936)

"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 'Ur-Leica'.


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 "Ur-Leica". 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 ratio--it 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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