Math in the Film Industry

By Taylor Whittemore

The film industry is a vast profession that encompasses several different types of occupations that each manage a different aspect of the film. Once the film is completed, it is sent to theatres around the country and sometimes internationally to produce profit. Since the entertainment industry is something people devote so much money towards, it has a box office gross of nearly thirteen billion dollars in 2014 alone. When people think about this expansive and expensive industry, they imagine the blinding lights, dedicated actors, and elaborate set. They rarely imagine how deeply math is integrated into the movies we watch with unparalleled fascination. Math plays a critical role in several careers involved in the film industry, such as producers, camera operators, costume and set designers, editors, and animators.

Producers are often given the task to control the specifics of the film, especially the budget. Needless to say, the budget includes a myriad of calculations. The producer must determine how much money is going to be spent on various aspects of the film while determining how much money is going to be set aside to pay the actors and crew. They must also seek out people who are willing to finance the film by making an investment in it, especially if it is a film independent of a large company. They continue to maintain and adjust the budget throughout the production of the film.

A film is comprised of the scenes that a camera captures, and therefore it is essential that the cameraperson captures the scene in the most effective way. Though the cinematographer technically decides on which angles should be shot, it is the cameraperson’s job to ensure that the video captured matches up to the cinematographer’s vision by using mathematics and, by extension, physics. They must calculate how the intended outcome will look with various filters, lenses, and film stocks. They also calculate variables such as exposure by using f-stops and focal lengths.

A film would be nothing without realistic sets or convincing costumes, and it is the task of set designers and costume designers to effectively convey these aspects over the camera. For example, could you imagine Star Wars: A New Hope without the Death Star, or Iron Man without the sleek design of Tony Stark’s metal suit? Though set and costume may often be overlooked, they are critical portions of the film, and there is also math involved with them. Sets must be carefully measured to ensure everything fits properly, and if it is a real setting being recreated, then they must be effectively scaled to fit the stage so the location still looks convincing. The attire a character wears must be carefully tailored to achieve the specific look the director is searching for. It has to be made to the actor or actress’ exact size, so multiple calculations are taken into account while creating or modifying costumes.

Editors are charged with the difficult duty of reducing countless hours of constant film to a movie generally between two and three hours long, and their job includes much math. When they trim shots, they may be cutting off mere milliseconds to help the different angles merge together seamlessly. An editor also creates the fades and dissolves that frequently create the transitions between scenes, and the speed of these effects depends upon how many seconds the editor tells the effect to take. For example, a fade that lasts five seconds will happen much quicker than a fade that lasts ten seconds.

However, animators are arguably those in the film industry who use mathematics the most, something several people do not expect because they imagine animators just sitting at the computer with lifeless eyes. However, an animator may use trigonometry, algebra, integral calculus, subdivision surfaces, and harmonic coordinates, depending on which element of animation that they are controlling. Subdivision surfaces are generally used while the animator is creating a setting, for they control the smoothness of the surface. This process incorporates much geometry, for it is a specific math inspired by the film industry that allows even an uneven surface to maintain a realistic smoothness. It was first used in Geri’s Game for the character of Geri. Integral calculus is used to determine how light reflects upon these smooth surfaces, and this is done by calculating how much light is

traveling from one point to another and later creating a rendering equation for this factor. Basic algebra is also incorporated in this process because it is used to give the light and objects additional shine and sparkle. Character movement is determined by harmonic coordinates, a type of math that applies to any dimension and uses Laplace’s equation. The combination of trigonometry and harmonic coordinates simplify how the characters move, and it allows the animators to move the characters with less effort. Lastly, the colors are created through a series of three numbers for pixel, and each number determines the amount of red, green, or blue in that particular pixel.

As mentioned before, math and film are not two things commonly associated with one another, but if a person is to look at the specifics of film, they will find that mathematics is integrated into various aspects of the different occupations. Producers, editors, costume and set designers, producers, and animators are all careers that have ample amounts of various mathematics. The types of mathematics involved also include multiple different types, ranging from the basics of algebra and trigonometry to integral calculus and harmonic coordinates, and the combination with the abovementioned math techniques and the film industry show a practical use that students often demand in a theoretical classroom setting.

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