The creation of today’s animated films, frequently hailed for their lifelike artistry, 1 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.
Answer
A
NO CHANGE
Answer
B
have relied
Answer
C
are relying
Answer
D
rely
A
NO CHANGE
EXPLANATION
Choice A is the best answer because the singular verb “relies” maintains agreement with the singular subject “creation.”
EXPLANATION
Choice B is incorrect because the plural verb “have relied” results in a lack of agreement with the singular subject “creation.”
EXPLANATION
Choice C is incorrect because the plural verb “are relying” results in a lack of agreement with the singular subject “creation.”
EXPLANATION
Choice D is incorrect because the plural verb “rely” results in a lack of agreement with the singular subject “creation.”
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