https://www.youtube.com/watch?v=5RL64wceWGI

When thousands of background characters were needed in "Wall-E," animators needed a solution other than individually drawing each robot. Of course, they didn't want to duplicate the same illustrations either. So the creative team at Pixar developed a custom system that added and subtracted parts from different robots to create several different characters.

It's a branch of mathematic calls combinatorics--the study of permutations and combinations--and it's one of the many academic lessons taught using real-world examples in filmmaking that are available through Pixar in a Box, a collaboration between Pixar Animation Studios and KhanAcademy.org that offers free courses aimed at middle and high school students.

“For years, we’ve heard from teachers at every grade level interested in creating animation-based curricula,” said Elyse Klaidman, Director, Pixar University and Archives. “We’ve wanted to provide free online resources for them, and Pixar in a Box makes that dream a reality."

What the online learning institution brings is an exciting behind-the-scenes look at animated filmmaking using lessons that combine science, technology, engineering, arts and mathematics concepts.

Other topics include how to use weighted averages to create "Toy Story's" characters like Buzz Lightyear and Woody, and how trigonometry is used to design the worlds featured in Pixar films.

Pixar in a Box launched Thursday and is accessible for free at KhanAcademy.org.