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Golden Ratio in Cinematography

Golden ratio, golden spiral, and golden ratio grids almost everyone is familiar with this technique, especially the photographers. It creates balance between the model/focus of the image and those that are at the edge of the spiral line. However, it is not only applied in photography, but also used in film making. Camera shots and angles are also being guided using the golden ratio. It gives the same essence as photography to film making, and it is one the techniques used by film production staff to produce a high-quality film.

Golden Ration influences the visual, aesthetics and cinematography of the film. It is one of the essential methods in controlling the visual language and proportions of objects in the film. The rule of thirds or the grids of Golden ration provides significant changes in the visuals of the scenes and using it accurately to emphasize the moods or the situations of the scenes can greatly affect the overall visual impact of the film. One of the ways it is applied in the film is by using the Fibonacci spiral shape over the frame.

By: Riel Anne Mag-isa

SOURCES:

Dempsey, J.(2020, October). The Golden Ratio in Photography: A Comprehensive Guide. Retrieved from https://www.photoworkout.com/golden-ratio-photography/#h-the-golden-ratio-in-photography-conclusion

Cartharis, G. (2014). The Golden Ratio & Cinematography. Retrieved from https://prezi.com/rgbo9he_rch1/the-golden-ratio-cinematography/

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Mathematics and outdoor photography experience

Mathematics can be seen in our every day lives. It can be seen in leaves and even tires of cars and trucks. By taking photos, we are able to help with education purposes in order to teach math. We are able to learn about symmetry, geometry, perspective just by looking at a photograph.

Without mathematics, our photos and structures around us would not appeal to the eyes. Structures would not be able to hold up if it were not for the math involved in it either.

Source:

Meier, A., Hannula, M. S., & Toivanen, M. (2018). Mathematics and outdoor photography experience – exploration of an approach to mathematical education, based on the theory of Dewey’s aesthetics. LUMAT: International Journal on Math, Science and Technology Education, 6(2), 146– 166.https://doi.org/10.31129/LUMAT.6.2.317

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An Ode to Math, Mathematics in Nature

In the world that we live in it often shows models, patterns and phenomena we see in mathematics. A vast majority of living organisms on earth show a form of symmetry in one way or another. Symmetry is all around nature, from microscopic organisms like volvox that exhibits spherical symmetry and to humans who gives example to a bilateral symmetry. Different organisms have their own certain symmetry depending on their own situation. An example can be a starfish with a rotational symmetry, and because of this will make attacking prey from multiple directions easier for the starfish.

Mathematical sequences is another concept that show up a lot in nature. The Fibonacci sequences a clear example, it involves adding the two previous numbers in the sequence to arrive at the next number i.e.: 1,2,3,5,8, etc. In nature this commonly known as the golden rule, a clear example of this is the number of petals on the flower.

Many animals use mathematical ratios as both for camouflage and predation. An animal like the diamondback rattlesnake use perfect geometric ornamentation to blend into their environment. These organized patterns and color schemes can help animals to also attract mates and repel predators. Mathematics also plays a big role in genetics and evolution. By using mathematical models, scientists are able to understand the population numbers as well as peoples physical characteristics within populations fluctuate.

By: Gab Baun

SOURCE:

Alex. (2019). An Ode to Math, Mathematics in Nature. Minute School. Retrieved from https://www.minuteschool.com/2019/09/an-ode-to-math-mathematics-in-nature/

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Math in Movies

It is safe to say that math plays huge role in movies, most especially in animated movies. According to computer scientist Tony DeRose of Pixar Animation Studios, “In each of these animated films constructed entirely on computers, trigonometry helps rotate and move characters, algebra creates the special effects that make images shine and sparkle, and integral calculus helps light the scenes.” The process of animation is a grueling job that would take up to four years from start to finish. Before we jump into animation in computers, artists first create thousands of hand-drawn pen-and-paper sketches or, Photoshop images and quick animations to flesh out the story.

DeRose continued by saying, "As the story starts to gel, the art department starts to fire up . . . to create characters and designs for the worlds the characters live in." The hand-drawn sketches become the backbone to build the digital characters, which is needed in the process to constructing physical marionettes with strings to govern their motions. The digital strings serve as a control system for animators to use to define a characters movement, from bending a knee to raising an eyebrow. A character would usually have 300 degrees of freedom with perhaps 700 controls, that’s about 700 strings an animator has to deal with.

Now let’s talk about the mathematics in animation, DeRose states a few examples like the simulation of how light bounces in a specific area (Integral calculus) to show a flat surfaces consistently (Subdivision surface) and making characters move smoothly (Harmonic coordination). The way light bounces around in an area is crucial in illumination. "Mathematically, for every point y and for every other point z, we need to compute how much light is traveling from y toward z, and we have to do that for every pair of points in the environment. In a continuous setting, this turns into an integral, the rendering equation," DeRose states. The geometric technique of subdivision surface is used by artists to create complex surfaces and complicated shapes efficiently on a computer without compromising its smoothness. This technique was inspired by the film industry, the technique of subdivision surface was first used in Geri’s Game (1999), which won an Academy Award. DeRose mentioned that Pixar recently turned to using harmonic coordinates because they are generalized barycentric coordinates that can be extended to any dimension, So basically it simplifies things for animators when they want to control the animated character.

With the rapid rise in animated movies, short films, and others, it is safe to say that mathematics is here to stay in the film industry. Who knows what the future will bring for animated films but one thing is certain for it to take a step forward mathematics is the key.

By: Gab Baun

SOURCE:

Derose, T. (n.d.). Math in the movies. Mathematical Association of America. Retrieved from https://www.maa.org/meetings/calendar-events/math-in-the-movies

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PHOTOGRAPHY: THE UNIVERSAL LANGUAGE

What is Photography?

Photography is the art of creating a picture by catching light with a camera, generally using a digital sensor or film. You may even picture wavelengths of light that are invisible to the naked eye, such as UV, infrared, and radio, with the correct camera equipment.

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Viewpoint

A lot of novice photographers probably take the most of their photographs straight-on. However, it is a good idea to start looking at subjects from different angles – switching up your position every once in a while can lead to very interesting results. There are 4 different viewpoints that photographers may use. Namely, bird’s-eye view, becoming the subject, eye level, and worm’s-eye view.

Bird's-eye view: When photographing through the bird’s-eye view, you shoot from above. This could be taken from up in the sky, such as when flying in a plane, or could simply be taken by standing on a ladder, slightly above your subject.

Becoming the subject: this point of view tends to be the most effective, especially when photographing people. To use this technique, photograph your subject from the point of view of the person interacting with the subject. For instance, if you were to take a shot of someone making dinner, take a photograph of the food as if you were the chef – perhaps even including hands in the foreground for reference. These sort of images make the viewer feel as though they are experiencing the scene themselves, and makes it easy to put themselves in the photographer’s place.

Eye level: Shooting at eye level is the most common way to photograph a subject. After all, it is typically the way we regard most subjects in our day to day lives, especially other people.

Worm's eye view: Photographing at worm’s eye view is done from below, as if you were a worm looking up at the world around you. This viewpoint makes all subjects look very large, even if they are very small in reality. As opposed to images shot from above, subjects presented in this way look as though they hold power over the viewer, and can seem very intimidating.

By: Bea Orense

Source:

4 Points of View in Photography | NYFA Photography. (2014, December 9). Student Resources. https://www.nyfa.edu/student-resources/point-view-photography/#:~:text=In%20relation%20to%20photography%2C%20’point,in%20when%20viewing%20a%20scene.&text=Subjects%20can%20be%20dramatically%20distorted%20simply%20by%20where%20you%20place%20your%20camera.

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Symmetry and Pattern

Repeating patterns and mirror-image symmetry look appealing when incorporated into your photos. Here’s a few tips on how to make the most of them. Our brains are wired to look for patterns and symmetry. There are a few main types of symmetry—all are really powerful for creating great photos. Symmetry can create balance in a picture and convey a sense of calm, even a sense of unease if everything looks a little too perfect.

Symmetry isn’t always caused by reflections; rotational symmetry is seen in the spiral shapes that are often found in nature, such as the arrangement of petals in a flower, or the curve of a snail shell. You can also find symmetry in the repeating patterns made by collections of objects – both man-made and natural. For example: logs in a woodpile, clay tiles on a roof, or tidal patterns in the sand.

By: Bea Orense

Sources:

Symmetry and Patterns . FUJIFILM Digital Camera X Series & GFX – USA. (2019). FUJIFILM Digital Camera X Series & GFX – USA. https://fujifilm-x.com/en-us/stories/beginner-month-1-composition-3-symmetry-and-patterns/#:~:text=Repeating%20patterns%20and%20mirror%2Dimage,when%20incorporated%20into%20your%20photos.&text=Symmetry%20can%20also%20create%20balance,It%20just%20feels%20right.

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Leading Lines

Leading lines are lines that appear in a photograph that have been framed and positioned by the photographer to draw the viewer's eye towards a specific point of interest. These lines draw the viewer’s eye in a specific direction or towards a specific area of the photograph. To use leading lines, it would be useful to understand the different types of leading lines and how they are best used. The categories of leading lines include: horizontal lines, vertical lines, diagonal lines, and converging lines.

Horizontal Lines: Horizontal leading lines are often used in nature and landscape photography. Because horizontal leading lines often stretch across the entire width of the image, they tend to be used when shooting with a wide-angle lens.

Vertical lines: Vertical lines shows power and hierarchy in a given photo. They draw the eye up or down within the frame and can be used to convey status within your picture. Vertical leading lines are often found in fashion photography and street photography.

Diagonal lines: Diagonal lines are used to create a sense of movement and change. Diagonal lines work to emphasize a sense of distance and often track from foreground to background. If you’re working with a large depth of field, try experimenting with diagonal lines to accentuate the sense of depth in your image.

Converging lines: If there are converging lines present in your frame, it’s best practice to situate the subject of the image at the axis of these leading lines. Converging lines are very effective at drawing the eye to the point of convergence and can be a strong compositional element to include in your photographs.

By: Bea Orense

Sources:

MasterClass. (2020). How to Use Leading Lines in Photography. MasterClass; MasterClass. https://www.masterclass.com/articles/how-to-use-leading-lines-in-photography#4-types-of-leading-lines-in-photography

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