How Mathematics is Used In Pixar

If you find your students asking when will they use mathematics in their life, then maybe you can answer them that they might want to be an animator or graphics artist at Pixar. 🙂 Pixar is one of the of the most popular animation studios in the world. It is the producer of Toy Story, Bug’s Life, Monsters, Finding Nemo, Brave and more.

Pixar uses a bunch of mathematics in making these animations. In the 7-minute video below, Tony Derose from Pixar explains how middle school and high school mathematics such as coordinate geometry and the concept of midpoints are used in Pixar animations. Watch the video and be amazed.

H/T: Great Math’s Teaching Ideas

Introduction to Coordinate Geometry

The Cartesian plane is one of the greatest inventions in mathematics.  Had Rene Descartes not invented the rectangular coordinate system, calculus would not have progressed immensely as we are using it in our time.

The Number Line

The coordinate system was derived from the correspondence between the real numbers and the points on number line.  Each point on the number  line corresponds to a real number and each real number corresponds to a point on the number line. The number line represents the ‘entirety’ of the real numbers.  By convention, the number line is a horizontal line where the negative numbers are placed on the left of 0, and  the positive numbers on the right. » Read more

Vectors, Parallelograms, and Commutativity

Basics of Vectors

Scalar quantities are quantities specified by magnitude. Mass, area, density are examples of scalar quantities.  There are quantities that have both magnitude and direction.  For example, when we say 2 kilometers east, 2 kilometers is our magnitude and east is our direction. Quantities with both magnitude and direction are called vectors.

In mathematics, vectors are usually represented by a directed line segment. The arrow  of the directed segment is called its head, and the other end is called its foot.

Comparing Vectors

Two vectors are said to be equal if they have the same length and the same direction. Plainly speaking, if we look at the geometric representation of vectors,  equal vectors have  the “same slope and the same direction (of the arrow). In Figure 1, it is clear that there only two equal vectors – vector u and vector v.

Figure 1

The negative of a vector is the vector  equal in length to a certain vector, but with opposite direction. For instance, in Figure 1, – u and u are negative of each other and vector u is also the negative of vector v. » Read more

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