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The creation of today's animated films, frequently hailed for their lifelike artistry, relies heavily on mathematics. Animators use algorithms, or sequences of mathematical steps, to create, for instance, the rounded shapes making up an old man's knobby knuckles or a young girl's bouncy hair. One of the algorithms now considered an industry standard repeatedly subdivides a polygon by splitting and averaging the midpoint of a line. Developed by Pixar Animation Studio's Tony DeRose, this algorithm eliminated the problem of discernible edges of polygons by replacing them with the seamlessly rounded curves of the parabolas that emerge as a result of the polygon subdivision process. Innovations such as DeRose's depend on an understanding of applied mathematics in areas such as geometry, linear algebra, trigonometry, and calculus.