Galina Mihaylova & Anton Ivanov

Photography and mathematics together

Following is intended rather for artists (and especially photography) and it would be good if they can last a long boring introduction for them. Well, there are pictures! It may be useful at all to create different compositional decisions.

That should be me ;-)
That should be me 😉

More than 25 years photography has been a hobby of mine. I had a whole laboratory copier, various chemicals tubs, dryers and whatnot.

My class-manager Ivan Stoyanov (slightly strange math teacher, whom I respect very much, however), I argued that the best mathematician among photographers and the best photographer among mathematicians. I am grateful to him for teaching me mathematics and today she is useful everywhere, it turns out, even in photography.

Recently resumed my passion to photography and found that mathematics and photography are pretty closely related.

Digital photography is something quite different from then, but there are many things in common. For example the composition.

Recently struggling with a Nikon D90 and impressed me something relatively small.

All photographers talk about “Rule of thirds” which identify sites for the most important objects in their composition. So I decided to join the so-called “grid” display, expecting to see a grid that divides the screen into thirds, as the instrument “crop” of Photoshop.

Yes, I did! There was a grid that divides the screen into “quarters”. Initially very irritated. I decided that this is a disadvantage. But something nagged me: “Well those from Nikon are not stupid people, they must have had something in mind .”

And I started to think.

Usually thinking too much I do not give, but this time I came to some conclusions that I would like to share with those who sacrifice themselves to read this long boring text.

Of the universe billions of years “build” their worlds in the form of repeated spirals.

Galaxy and spiral
Galaxy and spiral

For thousands of years artists have realized the harmony in nature and create their works, intentionally or not, the use of so-called “Golden ratio”:

The formula for the golden ratio
The formula for the golden ratio

It is approximately 1 : 1,618.

This ratio is defined much later, although it is often used in ancient art.

In the Middle Ages an amateur mathematician (actually he is a merchant from Pisa) – Leonardo Fibonacci, along with a exercise propagation of rabbits, sets out a series of numbers 1, 1, 3, 5, 8, 13, 21, 34, etc. Characteristic of each subsequent number is that it is in the “golden ratio” of the previous one.

He was a modest man than this treatise is lost somewhere reserved only excerpts. Promoted from French mathematician Luca much later , by calling the name of Fibonacci things associated with its numbers – ” Fibonacci Line “, ” Fibonacci Ratio ,” ” Fibonacci Spiral ” etc.

Us in the case we are interested in “Fibonacci spiral”. That is what it is.

Fibonacci Spiral
Fibonacci Spiral

Rectangle that is listed is a “golden ratio” of countries – 1:1,618.

By “weight” a feature in it that separates it in the “golden ratio” (AH:HB = 1:1,618), the smaller part is such a rectangle that is split in the same way, etc. to infinity.

Proportions in the Fibonacci spiral
Proportions in the Fibonacci spiral

This infinity is actually the point of “endless attention” to our vision and he unconsciously moving in the same law that created this spiral until it stops at “infinity” at one point (intersection of green dotted lines).

Vertically inverted Fibonacci spiral
Vertically inverted Fibonacci spiral

In this image I remind you that the spiral can be turned around and turned horizontally and vertically without showing any options. It is unnecessary.

I will not describe details of the “Fibonacci spiral” probably “Google” knows about it more than me, and anyone can ask.

For us the important thing is that artists (whether sculpture, painting, music, etc.) put in composing their works often using “golden ratio” (some even called it “divine”).

What happens in the so-called in photography “Rule of thirds”?

Well, pretty much the same. The intersection of the lines dividing the image into thirds, which is appropriate to “focus” the gaze of the viewer is located very close to the points set for “infinite care” of Fibonacci spirals (look at the pictures with the yellow lines):

Rule of thirds and the Fibonacci spiral
Rule of thirds and the Fibonacci spiral
Rule of quarters and Fibonacci spiral
Rule of quarters and Fibonacci spiral
Rule of thirds and the Fibonacci spiral (vertical)
Rule of thirds and the Fibonacci spiral (vertical)
Rule of quarters and Fibonacci spiral (vertical)
Rule of quarters and Fibonacci spiral (vertical)

According to the “Rule of thirds” points of attention are the intersections of the yellow lines , and points of attention as the Fibonacci spiral are staging points shrink to a point

In the next picture you can see orange lines (look them now). They are like the “grid” display Nikon D90 – divide the image into quarters.

Obviously, the intersection of the orange lines are located closer to the point of care set by “Fibonacci spirals”. I.e. Japanese from Nikon are not wrong.

Of course, an “array” of four coils, points of focus and many other information would be more confusing to the photographer, rather than supporting it and not have painted this grid with spirals, just four lines.

This is my answer to the question why Nikon D90 display is divided into quarters instead of thirds. Or at least this is my opinion. (If it was in Bulgaria, I’d rather decided that after a glass of brandy designer is not counted correctly bars, but it is still not our dear homeland but Japanese corporation.)

Anyway, since I considered these things with the Fibonacci spiral, it’s easier to build a composition of photographs and drive the viewer’s eyes to “crawl” the entire image like corkscrew or on green dotted lines (if the objects are linear) until it reaches the most important subject – the center of attention.

At least try. I wonder whether no longer cropped image format 8 x 13 cm – this is the closest ratio in whole centimeters to 1: 1,618.

I do not want to get into disputes with hardened supporters of the “rule of thirds ” – space is available for all. You can never find an exact match as photographic as to comply with one or another rule. Rules sometimes violated to achieve originality and creativity.

I suggest you just a different look at the composition solutions. Still, I’m curious what other people would say, especially professional photographers and advanced amateurs and would expect any feedback – and critical and laudatory – the more opinions, more accurate decisions.

p.s. Until recently, I thought I invented something… but on the Internet on this subject was written, written …. example here:

Divine Composition With Fibonacci’s Ratio

There are three interesting movies in an interesting article.

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