The Science Behind Pixar

See all Pixar's characters at www.pixar.com

Many people simply aren't sure what applied mathematics can accomplish, or, which accomplishments required applying challenging and exciting mathematics. One wonderful example of creators using mathematics to perfect their craft is Pixar Animation Studios. They're the folks responsible for fan-favorites Toy Story (1995), Finding Nemo (2003), Up (2009) and, most recently, the wildly popular Inside Out (2015).

That's why we recommend you check out the newest exhibit at Boston's Museum of Science: The Science Behind Pixar.

Enjoy a unique, first-time look into the Pixar process, and explore the science and technology behind some of the most beloved animated films and their characters with the world premiere of The Science Behind Pixar. This interactive exhibition showcases the science, technology, engineering, and math (STEM) concepts used by the artists and computer scientists who help bring Pixar's award-winning films to the big screen.

You'll definitely have the opportunity to explore and use mathematics to create virtual 3D models.
If you're serious about 3D modeling and mathematics, check out Matrices, Vectors and 3D Math with Matlab® or an Introduction to Groups, Rings and Fields here.

read more and purchase tickets here
read more about the Museum of Science here

What's your favorite Pixar movie? Which movie do you think was hardest for animators to create? Let us know in the comments!

Problem of the Week

This week's problem's solution is actually easier to state than the problem itself. That isn't to say that it's easier to arrive at, though! There is not a whole lot of theory involved at reaching the solution, only a few clever insights. Of course one could use combinatoric to explore every conceivable combination of the 4 numbers to arrive at a solution, but even in this instance, it would be just trial and error.

Drum roll, please...The solution is:

6/(1-(5/7))

We hope that you enjoyed this problem! We have problems like this up every Monday; just check out the Center of Math Twitter.

Math Minds: David Craft

Dr. David Craft is a modern-day renaissance man. He graduated from Brown University with a degree in Mechanical Engineering, then went on to a mathematical Ph.D. in Operations Research from MIT, and currently works with Harvard Medical School in oncology research. Among his many interests are Gallery 263, foraging, and creating music. He is also working on a new book- it will be titled Something About Infinity- and it presents interesting mathematical topics in an enjoyable, easy read.

He sat down with Tori and Zach this past week to discuss the math side of his life, and to get his perspective on the challenges of math modeling in medicine.

Problem of the Week

Throwback Fact: Sally Ride in Space

Sally Ride in space.
image: commons.wikimedia.org

On this day in 1983, Sally Ride became the first American woman in space (Valentina Terishkova was the first woman in space, as part of the Soviet program in 1963). In her biography on NASA's site, Dr. Ride's listed experience includes earning a Physics Ph.D. from Stanford University, developing the space shuttle's Canadarm arm, two space missions, and serving on the committee investigating the Challenger disaster.

Ride was not a mathematician, but an astrophysicist. However, I'd like to take the time to chat briefly about mathematics as it relates to space.

Counting Systems: Maya

The great pyramid at the Mayan city Chichen Itza
(it was featured in one of our favorite blog posts)

The Region: The Mayan civilization can be split up into several distinct periods: the preclassic, classic, and postclassic. During the final period, explorers from Western Europe made their first contact with the Mayan people (around 1500 CE). 

Over the 3500 years that the Mayan culture was prominent, the lands under their control remained expanded and shrank several times. They were limited to the Yucatan Penninsula (present day, a part of Mexico) but had strong ties to the Olmec and Toltec cities in surrounding Mesoamerican lands.

The Numerals: In many ways, the Mayan numeral system is more intuitive than our own. They used a Base-20, or vigesimal, system.

Problem of the Week

Good morning from the Center of Math! This problem today seems like a geometry problem when you first look at it, but I solved it with calculus. Take a look at the question below, which I posted to our Facebook, Twitter, and Google+ pages.

You can click on any photo in the post to expand

And as every week these past six months or so, I've written down my solution. Take a look below...

Throwback Fact: German Tank Problem

A WWII-era German Tank
image: commons.wikimedia.org

Last Saturday, June 6th, marked the 71st anniversary of D-Day, when the Allies invaded the beaches of Normandy and began to turn the tide of World War II. So, though it is not linked to any particular date in math history, it's fitting that we showcase a WWII era math problem.

The German forces had an advantage that the Allies had to overcome: more, and technologically superior, tanks. Knowing how many tanks the Germans were producing was the first step to figuring out how to take care of this threat. So, the Allies tried conventional methods of gathering intelligence: interrogation, spies, and decoding messages.

Counting Systems: Ancient China

Shards of the Shang Oracle Bones

In the 1890s, an archaeological dig in the Henan province of China unearthed a treasure trove. A set of bones carved with ancient text were dug up where the capital of the Shang Dynasty (1600 - 1046 BCE) was located. The oldest inscriptions that are recognized as Chinese were carved in about 1200 BCE on these ancient "Oracle Bones."

The Region: Chinese history is vast. There have been groups living in China for thousands of years, and we've discovered written records about the established dynasties on the Eastern side of the country dating as far back as 1200 BCE. The cultural center of China was naturally isolated, with mountains on the west and water to the east. This allowed Chinese numerals and mathematics to develop naturally, without much influence by other number systems, for centuries.

Math Changes Quickly.

A few days ago, I stumbled upon this article. The penmanship is fascinating, and those boards must have been covered up right around Thanksgiving! But my favorite picture from the article was the number wheel, which "apparently was used to teach multiplication tables." I've recreated it on our chalkboard to get a better look at it.

I realized that I've studied the differences in mathematics across thousands of years. I gave a discussion about the Babylonian number system recently, and a discussion on Ancient Chinese numerals is coming soon. But the fact that math can change so much in 100 years that I don't immediately understand this multiplication wheel is incredible!

Problem of the Week

Good morning from the Center of Math! To start off your week, we have a Problem of the Week that we've posted to Facebook, Twitter, and Google+. I learned about this statistics/logic problem from our summer intern, Or. We've decided to share it with you this week!

Click on any image in the post to expand.

There are several different ways to approach this problem. The method I chose was...

Throwback Fact: Emmy Noether's Math Journey

Emmy Noether

The way we name proofs in mathematics, most often after their founder, immortalizes mathematicians who could otherwise slip into history unnoticed. But 96 years ago today, an event occured that helped to keep one particular female mathematician from obscurity.

Emmy Noether (1882 - 1935) almost missed her chance at mathematical fame. Born to a Jewish family in the German town of Erlangen, Noether showed few signs of her mathematical talent until she reached a college age. Noether originally planned to learn to teach English and French, but she attended math courses at the University of Erlangen where her father lectured. There, she earned her doctorate in mathematics in 1907, and worked at the same university for 7 years, but didn't earn a single payment for her research. 

8 Tips for Perfecting the SAT Math

This Saturday, June 6th, thousands of students across the Unites States (and some abroad!) will assemble early in the morning to take the last offered SAT exam of the season. In order to prepare yourself as best as you can, why not read up on some tips and tricks? These will help anyone planning to take the exam on Saturday or in the future. It will help ACT test takers as well- the math sections test the same subject areas, just in a slightly different way.

I took a number of steps to prepare myself for the exam date when I was in highschool. Some of these  tips will seem like common sense- and they are!- but students sometimes need to be reminded of the little things. While I can give some advice regarding the entire test, I won't try to give specific tips in the reading and writing sections. Let's face it- math is my forte. Without further ado, here are my tips and tricks for preparing as best as you can for the SAT math section.

Problem of the Week

Good morning from the Center of Math, and welcome to June! It's a rainy morning here in Cambridge. It's a coincidence that our Problem of the Week (which we posted to Facebook, Twitter, and Google+) involves water. It's slightly deceptive, so be careful when reading it:

Click on any picture to expand!

Ok, so this problem has a little more physics than our usual problem of the week. But it's nothing we can't handle. Take some time to try it yourself! My solution is below: