Cinemath and ratios
CINEMA AND RATIOS
The Golden Ratio in Cinema
In this activity we will connect Cinema and Geometry by working with proportions, and specially with the Golden Ratio.
We would like to start reminding what the golden ratio is:
Also known as the Golden Mean, Phi, or Divine Proportion, this law was made famous by Leonardo Fibonacci around 1200 A.D.
He noticed that there was an absolute ratio that often appears throughout nature, a sort of design that is universally efficient in living things and pleasing to the human eye. That is the reason of the “divine proportion” nickname.
Previously, Fibonacci discovered the sequence that has his name, and that gave rise to the golden ratio later on.
Fibonacci´s sequence is the numerical sequence:
It is an infinite sequence in which each term is found by adding the two numbers before it. For example 1+1=2 or 13+21=34. The ratio between two consecutive numbers is aproximatly 1,618034, the called “golden number”. This means that if we divide each number by the previous term of the sequence we will get that “sacred” number.
Let´s try to do it more visual. We can translate this ratio to a rectangle whose sides are two consecutive numbers of the Fibonacci´s sequence.
If we divide the rectangle using the sequence:
And finally, if we draw a line joining all the squares, we get something similar to this spiral:
We can find this golden ratio in multiple places in Nature. For example, that spiral, called the Golden Spiral, can be found in the sunflower seeds, in seashells…Even we can find the divine proportion in our own body!
We can also find the golden ration in many human constructions. Since the Renaissance, artists and architects have been designing their work to approximate this ratio of 1:1.618.
It is found all over the Parthenon, in famous works of art like the Mona Lisa and the Last Supper, and it is still used today. The divine proportion has been used by companies like Apple to design products, and as you can see, it has been used by Twitter to create their profile page.
CINEMA AND PROPORTIONS
Cinema and Photography are closely related with proportionality.
The photographies that we take are framed in a rectangle of precise proportions. The dimensión of the screens in a TV or in a cinema room are not randomly chosen.
The photographic format that we know was developed by Oskar Barnack, who chose it to build the first 35mm camera, "the Leica". The negative with proportion 3:2 or 24x36 has been with us since then, and it is probably because of its similarity with the golden ratio.
Over the years, the cinema screens have been widening to a panoramic view, and in the last years the ratio 1,85 to 1 is imposing thanks to the influence of Hollywood. However, the film format which is closest to the golden ratio, is the one used in the European cinema in the last decades.
Besides the screen ratios, the divine proportion is frequently used in the composition of the images that will be taken, both on photographs and on movies, because cinema is photographs in movement.
HOW TO USE “THE GOLDEN RATIO TO IMPROVE OUR PHOTOS
When applied to photography, this ratio can produce aesthetically pleasing compositions that can be magnets for the human subconscious.
We naturally prefer to look at an image that is balanced and harmonized, and the Golden Ratio provides this
Frequently, we look for the Golden Spiral without realizing it, because golden ratio is in Nature and pictures taken using this technique seems to be more natural. For example, we can find it in this picture.
To learn how to use this ratio in a photo composition we need the rectangle we have used before and we will put four golden spirals, each one with the origin in a corner.
In this picture we can observe what happens when we mark in red the centre of each spiral.
The points we have obtained are close to the “sweet spots” of the Rule of thirds, a famous rule in Photography.
It is said that the Rule of Thirds was designed as a simple way for photographers to locate the sweet spot, the point at which the human eye is first drawn to, of the Golden Ratio.
This Rule is used in Cinema and Photography to organize the objects in an image or scene. We can find some examples in the European Cinema:
These are some techniques of composition using the rule of thirds:
 Sweet Spots: The main points will be close to the thirds and their intersections. So we will collocate there the principal elements (the audience will pay more attention to those points unconciously).

 Closeups: Closeup portraits will be more striking (eyecatching) if we make coincide the eyes with the thirds.
 Horizon / Ground: We will try to make coincide the horizon with one of the thirds.
 Position: It is important to decentralize the objects horizontally. In movies, people do not usually appear in the centre of the screen, but in one of the thirds.
When we decentralize an object or a person we have to consider what they are doing. If, for example, a person is moving we will leave empty space in front of him, the same if it is a vehicle in movement.
Anyway, sometimes we will not use these rules. It depends on the feelings and messages we want to transmit. Sometimes to focus on the centre can be a good solution.
In cinema, the British director Kubrick, is a good example of centralizing a scene, as we can appreciate in the following video.
https://www.youtube.com/watch?v=flq0t4jrqJQ
ACTIVITY
Now it is time to put into practice what we have just learnt. So we will become directors and actors.
We will shoot a scene of Cinema Paradiso movie. Let´s watch the scene
In this scene there is two main roles: Salvatore and Elena, and one extra  the penitent  that can be performed by a boy or a girl. The rest of the team will be the director and their assistants.
Don´t worry about the script, we will give you one. Anyway you can improvise, whenever you keep the essence of the scene.
Use your mobile to record it, and send us to cinemaths@gmail.com
Do you want to watch the scene again?
Any question?