That's All Folks!

Yesterday was the last live broadcast of The College Mathline. We have been on the air for 9 semesters now and aired a total of 96 episodes.

A big thank you to all the students and viewers who called in or emailed with questions and who worked on our contests! Thanks also to the crew that worked on the show.

All of the episodes are archived at www.collegemathline.com and will remain there for the time being if you want to check any of them out. We'll keep the blog up and running too.

Good luck with your math everyone!

hot air balloons

For our last episode, we showed some of the math that helps explain how hot air balloons rise through the air. Most people know that hot air rises, but why? The Ideal Gas Law (pV = nRT) says that if the pressure inside the balloon doesn't change (true) and the volume inside the balloon doesn't change (also true) then an increase in the temperature will cause a decrease in the number of air molecules occupying that space. That means the heated air is less dense than the outside air. A principle stated by Archimedes explains that buoyant force pushes the less dense air upward.

The balloons need to be quite large because this upward force is quite weak, a fraction of an ounce per cubic foot of air. But if you make the balloon large enough (many balloons are 90,000 cubic feet) the buoyant force can be great enough to lift the balloon (800 lbs) and its passengers.

We also showed an equation that can give, approximately, the amount of lift to expect from heating the air a certain number of degrees.

For additional info:

Wikipedia entry on hot air balloons

A nice explanation of the math and physics involved with balloons at How Stuff Works

new contest!

One last contest for everyone!

Some algebra may be required! If you figure it out, you can be our official winner by calling us and giving us your answer on our final live broadcast, Wednesday April 15. The phone number is (888) 762-1489. Good luck!

unmanned aircraft

This week we showed our visit to Northrop Grumman where we talked with several of their engineers and employees about how math is used in their design of unmanned aircraft, especially the new X-47B jet being developed. One of the key features of these craft are numerous control systems that are used to pilot the craft. Each control is basically a closed loop system that constantly compares the current state of a quantity to a goal value and makes adjustments. This happens many times each second and allows the jets to navigate and land smoothly and safely. One kind of control used is called a PID controller which stands for Proportional-Integral-Derivative. Yes, that's integral and derivative straight out of calculus class. The control uses these three quantities in combination in order to make adjustments quickly but smoothly that avoid overshooting a target value.

We also learned that Northrop Grumman is in need of talented engineers, even in the current economic environment. And, the people working there love what they do! See what math can do for you?

For further reading:

Northrop Grumman's X-47B site

career opportunities at Northrop Grumman

Wikipedia entry on PID controllers

Legos & math

For our April 1 episode we talked with Eric, one of Legoland's master model builders. He showed us how mathematics comes into play with his work every day. The dimensions of Lego bricks are based on a 5:6 ratio which he must keep in mind as he plans and builds his models, especially when pieces will be used in atypical ways. He even has special rulers and graph paper to help with the ratio. We also talked about how Lego models, built from rectangular bricks but forming curved shapes, are illustrations of the approximation and limit process from calculus that we use in defining double integrals.

Plus, it was April 1, so April Fools Day pranks and jokes abound!