College Mathline

That's All Folks!

2009-04-16T00:59:00.001-07:00

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

2009-04-15T22:47:00.000-07:00

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!

2009-04-09T12:02:00.000-07:00

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

2009-04-09T11:50:00.000-07:00

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

2009-04-01T19:50:00.000-07:00

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!

Measuring water purity

2009-03-18T22:54:00.000-07:00

This week we showed our interview with one of the chemists, Joel, working at Encina Wastewater Authority in Carlsbad, CA where they treat wastewater so that it can be returned to the ocean. Water samples are tested for the amount of suspended solids as it arrives at the facility and at various stages throughout the treatment process. Joel showed us how he determines the level of solids, measured in milligrams per liter, and what math he does in the process.

The incoming water typically measures between 200 and 400 mg/L, and it leaves the facility at less than 5 mg/L before it heads to the ocean. That's a 99% reduction!

We also mentioned the March Madness men's college basketball tournament beginning tomorrow. Many organizations offer cash prizes if you correctly predict the winners of all the games (there are 63 games in the tournament). One site is offering $12 million! Are they confident they won't have to award any money? Probably! On the program, we showed the astronomical odds of correctly picking all the right winners. No one has done it yet! Here is an interactive bracket you can fill out for fun on ESPN's website.

new contest!

2009-03-04T23:49:00.000-08:00

As described above, we have a new contest running. You may need to use a little algebra! If you figure it out, you can be our official winner by calling us and giving us your answer on our next live broadcast (March 18). The phone number is (888) 762-1489. Good luck!

Ocean waves

2009-03-04T23:35:00.001-08:00

On this week's broadcast we discussed many ways in which mathematics is used in the study of the movement of water in the ocean. It turns out that this is a pretty complicated issue. There are partial differential equations that are used to describe fluid flow, but solutions to these equations have been elusive thus far. Computers are used to estimate approximate solutions with research continually done to improve the results.

We also talked about how water waves resemble the graph of the sine function from trigonometry. A more accurate model is a "trochoid," the path formed by a point on a wheel as the wheel rolls along the ground. Both the sine graph and trochoids are based on circular motion which isn't too much of a surprise since ocean water actually moves in small circles as the shape of a wave moves across the surface.

For further information check out these links.

animation of ocean wave

Wikipedia entry on ocean waves

detailed article from SIAM on mathematics and the oceans

Feeding Whales

2009-02-26T10:10:00.000-08:00

For our first episode of 2009, we visited SeaWorld in San Diego and met with one of their trainers Mike. We got to help feed the Beluga Whales there and Mike talked with us about the math involved in the animals' diet. The total amount of daily food intake is determined for each animal from several different variables such as gender, weight, age, and time of year. Then proportions of four different kinds of fish must be made for each animal to correctly balance different nutritional elements. These are basically "mixture problems" from an algebra class.

We also talked about methods to estimate the size of crowds, inspired by the Amgen Tour of California bicycle race that finished in Escondido over the weekend. The claim was that 300,000 spectators witnessed the final leg in San Diego county and over 2 million watched the race throughout California. How did they come up with those numbers?

This week's links:

SeaWorld San Diego

Wikipedia entry on Beluga Whales

Amgen Tour of California bicycle race

Math Questions Spring 2009

2009-02-23T11:15:00.001-08:00

You can leave math questions for us here, as comments to this post, and we will solve them on the broadcast each Wednesday.

If you aren't able to see the program live, record it for viewing later or you can watch it online when it is archived at www.collegemathline.com.

Mathline returns this week!

2009-02-23T11:08:00.000-08:00

The College Mathline returns to its live broadcasts this Wednesday, February 25, at 5:00 PM.

This semester the program can be viewed on AT&T U-verse channel 99 or as a live webstream available at www.collegemathline.com. The show is also rebroadcast on Saturdays at 6:00 PM.

Have a math question for us? Call us live during the program at (888) 762-1489. Or you can post your question here on the blog before or during the broadcast and we will solve it on the air. You can also email us your question at mathline@palomar.edu. If you aren't able to see the program live for the solution, record it or watch it online once it is archived at www.collegemathline.com.

on hiatus

2008-11-26T09:25:00.000-08:00

We are ending the season a little early this semester. The television program is now on winter break. We expect to be back on the air in February. In the meantime, we encourage you to leave us feedback here if you have any comments or suggestions about the program. As budgets tighten for everyone, it is helpful to hear from anyone who benefits from the program!

Last week we unfortunately experienced technical difficulties during our last show of the year and the signal got knocked out at the end of the hour. We apologize for that, hopefully that won't happen again!

We wish everyone a great Thanksgiving and holiday season.

GPS

2008-11-19T10:08:00.000-08:00

If you have used a GPS navigation system in a car, you know how valuable it can be. How does that little electronic device know exactly where you are? It relies on a system of satellites orbiting the earth about 12,600 miles up. At any location, the GPS receiver should be able to see at least 6 of these satellites, each of which transmits information about the locations of all the orbiting satellites along with precise time stamps. The GPS receiver is not capable of communicating back to the satellites, so it listens to these signals and, with lots of mathematics, determines its location.

Specifically, the GPS receiver can determine the synchronized time by comparing messages from different satellites. It can then determine precisely how long each signal took to travel from the satellite to the receiver. The signals travel at the speed of light, so a quick computation tells the device how far away it is from each satellite. On the program this week we showed how having only this information--the distances from several satellites--the GPS receiver can determine exactly where it is on the planet using a process called trilateration. How many satellites are needed to make this happen? The more you have the better, but a minimum of 4 is required (3 if you use information about your elevation on earth).

For more information, check out this very detailed Wikipedia entry.

Tricked out Hummers

2008-11-12T11:40:00.000-08:00

This week we showed our recent visit to Predator Motor Sports where they retrofit various Hummer vehicles with more powerful engines and upgrades that makes them not only faster and more powerful but also greatly improves their fuel economy. How do they pull this off? As we saw, there is some math behind the scenes.

As part of the process, they tweak a variety of settings in control modules on a vehicle and then study the interrelated effects on about 150 data tables. A computer helps them with the math between all the variables. One of the most important things they watch is the horsepower of the engine and the vehicle. A dynamometer ("dyno") is used to measure torque and RPM, and a mathematical formula converts this to the horsepower measurement.

They also have to fit a larger engine with larger components into the original space, so carefully made custom pieces with precise angles and measurements are required that they make themselves.

You can check out Predator Motor Sports at their website here.

One more link: Wikipedia entry on how dynos work

Feedback wanted!

2008-11-05T16:05:00.000-08:00

As we all know, times are tough economically, and Palomar College is getting hit with budget cuts like everyone else. So, some programs may have to unfortunately be cut. If you would like to see the College Mathline continue, please let us know by leaving a comment here! (Click the "comments" link below.) You can also email us at mathline@palomar.edu.

Thanks!

Water treatment

2008-11-05T10:16:00.000-08:00

This week we showed our visit to the Encina Wastewater Authority in Carlsbad, CA where they treat wastewater so that it can be returned to the ocean. Perhaps that's something that you haven't given much thought, but it was quite fascinating to see how they accomplished this task and they have a very impressive facility. And yes, mathematics factors in to many of the processes happening there.

Most of the work treating the water is done by bacteria and other microorganisms. The staff must constantly monitor and adjust the ratio of these organisms to the amount of solid "food" coming in. There is a large aeration tank where the organisms consume the waste followed by a secondary tank where the organisms and matter clump to form an "activated sludge." Some of this sludge is directed back to the aeration tank as needed to keep a 0.5 ratio. In the end, 100% of the sludge is used internally or processed into fertilizer.

After the microorganisms have done their work, the water is ready to be returned to the ocean, after being tested of course.

You can find more information on the Encina Water Authority at their website.

Happy Halloween!

2008-10-29T23:48:00.000-07:00

Some Pumpkin Pi for you, of course! This week we had a festive episode with a spooky set and costumed crew. We even investigated strange apparitions in the studio. We still did lots of math, as usual, and we had a winner for our contest.

Sailplanes and Gliders

2008-10-22T00:24:00.001-07:00

Aviation in general involves plenty of mathematics, but we recently talked to Bret at Sky Sailing about how math comes into play in the piloting of sailplanes and gliders. This week we showed our interview with Bret and he explained many different instances of how math and mathematical thinking are necessary skills for flying these amazing crafts. He talked about making sure that the center of gravity of the plane with its passengers is within a certain range; otherwise the plane can be out of balance and can't fly. He also mentioned the "glide ratio" of a plane which is very similar to the algebraic concept of slope. Wind affects a plane's ground speed and navigation, so the speed of the wind must be factored into distance computations and navigation decisions. Brett also mentioned that he is constantly evaluating angles to locations on the ground while in the plane, especially when landing. It's probably no surprise that he also deals with conversions between units as well.

It is well worth visiting Sky Sailing in Warner Springs and going for a ride!

More information: Wikipedia entry for sailplanes and gliders

new contest

2008-10-20T14:45:00.001-07:00

We have a contest running right now as outlined in the graphic above. You can't change the position of the digits, but you can use as many of those mathematical symbols as you like. You can even put parentheses around digits, like ( 5 4 ), and consider that "54." And if you haven't seen that symbol "^" used before, that is used for exponents. (So 4^3 means 4 cubed.) We know of one way to do it, but there are probably many correct answers. If you find one, you can be our official winner by calling us and giving us the result during the live broadcast this Wednesday, October 22, 5-6 PM. The phone number is 1-888-762-1489. Good luck!

Archimedes Screw

2008-10-15T11:04:00.001-07:00

The Archimedes Screw was invented over 2,000 years ago and is still in use today! Its purpose is to transfer water to a higher elevation, and it works by turning a large, tilted screw so that the blades of the screw scoop up water, the water sits between the blades as it rides upward, and it is spit out at the top. The photo here was taken at SeaWorld in San Diego where they use two of these devices to push water uphill for their Shipwreck Rapids ride. We spoke with an engineer at SeaWorld about the Archimedes Screws in use there and the mathematics involved in them.

The screw only works if it is tilted within certain angles, so the concept of slope comes into play, both for the cylindrical screw and the blades themselves. The blades form a mathematical shape called a helix, and if you look at the blades from the side, the contours of the helix match the graphs of sine waves. These sine waves must have a downward slope as they cross the axis of the screw in order to hold water as the screw turns.

During the broadcast we mentioned a research paper (link below) that determined the optimal design for an Archimedes Screw using lots of calculus and 3D graphs. Don't worry, we talked about the highlights on the program which can be viewed once it is archived at www.collegemathline.com.

This week's links:

Wikipedia entry for Archimedes Screw

Animation of an Archimedes Screw pushing a ball uphill

research paper by Chris Rorres (pdf document)

f/stops in Photography

2008-10-08T11:56:00.000-07:00

When you take a photograph, there are mainly two elements controlling how much light is sent to the film or digital sensor. One is the shutter speed, which is simply how long the sensor or film is exposed to the incoming light, and the other is the aperture or "f/stop." The f/stop is a measure of the lens opening itself. The larger the opening, the more light comes in (and the faster the shutter can be). The f/stop is actually a ratio of the focal length of the lens (the distance between the lens and the film or sensor) to the diameter of the lens opening. So the larger the opening, the smaller the f/stop. Some of the fancier cameras, like SLRs, let you choose these settings yourself if you wish. Even the pocket digital cameras are using these settings, they are just done automatically for you. In fact, many photo viewing software applications can tell you what shutter speed and f/stop the camera used when it took the photo.

Each time you take a photo, you or your camera must make a choice between a larger opening and a shorter shutter time or a smaller opening and a longer shutter time. Either way you can get enough light for a good picture. So what is the difference? If you use a long shutter time, a moving object will look blurry. If you use a large opening, the depth that can remain in focus is much shorter. For instance, the first photo of the watering can uses an f/stop of 5.6. The chair behind it is quite fuzzy. The second photo, with an f/stop of 16, has the chair in sharper focus.

If you look at the available f/stop numbers for a particular lens, you might find the numbers mysterious. You will often see a progression like 2, 2.8, 4, 5.6, 8, 11. They almost seem random. In fact, there is logic to it! These are the values of the f/stop ratio where the lens opening doubles in AREA (not diameter!) each time. This lets in twice as much light. Remember that the area of a circle is based on the square of the radius, so if you want the area to double, you can't double the radius. In fact, you would need to multiply the radius (or diameter) by the square root of two. And that multiple, root 2, is exactly where the progression of f/stop numbers comes from.

Here are some links if you want to learn more:

Wikipedia entry for f/stop numbers

A very detailed (and good) explanation of f/stops and the math involved

Math Questions Fall 2008

2008-10-06T09:17:00.000-07:00

You can leave math questions for us here, as comments to this post, and we will (hopefully!) solve them on the broadcast each Wednesday.

Mathematics and Legos

2008-10-01T20:08:00.000-07:00

We're back for our 8th semester broadcasting! And during our first episode, we showed an interview with one of the Lego model builders, Eric, at Legoland California. His whole job is building things out of Legos, how is that for a cool job? If you visit Legoland, you will see "Miniland," where they have recreated cities out of Legos in amazing detail.
Eric described how he has to think mathematically every day at work, including determining scales, creating designs and blueprints, and estimating how many Lego bricks to order for a project. He showed us his most recent project: a Lego version of the extraordinary Burj Dubai skyscraper in the United Arab Emeriates which will be finished next year.
The image at the left shows the Lego version with the actual building in the background.

This week's links:

Miniland at Legoland California

Burj Dubai official website

Wikipedia entry for Burj Dubai

We're (almost) back!

2008-09-17T13:51:00.000-07:00

The College Mathline is returning to the airwaves. Our first live broadcast is Wednesday, October 1, 5:00pm. We have lots of cool things lined up for everyone this semester!

summer break

2008-05-20T20:57:00.000-07:00

We are taking a break from our TV broadcasts for the summer, but we will be keeping up with this blog, so feel free to leave any comments or suggestions. We will be back with live broadcasts in the fall.

Each week on the TV program we highlight some mathematics as seen in the "real world," and if you have any ideas for these segments we would love to hear them. Perhaps you use math in your job or hobby, or know someone who does. We could even visit a workplace and talk with people about how mathematics is used, as we have in the past.

Music and Mathematics

2008-05-14T09:22:00.001-07:00

There are many connections between mathematics and music, and it seems that many people who enjoy mathematics also play musical instruments. This week we looked at the tones we hear in almost all western music. Almost all western music uses 12 tones in a scale. Why 12, rather than some other number? The tones we hear are based on sine waves of different frequencies, and it turns out that the combinations of tones that sound most pleasing to us are based on ratios of small integers. Splitting one octave into 12 equal steps gives a very close approximation to these ratios. Still, there are many other tunings used in other countries around the world.

This week's links:

a short and sweet look at our 12 tone scale

Wikipedia entry for Music and Mathematics

Hear a tuning based on pure ratios ("Just Intonation")

The Normal Distribution

2008-05-07T20:39:00.000-07:00

The normal distribution is a probability distribution shaped like the classic bell curve. You will see a curve like this if you make a chart of, for example, the heights of a large number of adult women, you will see this curve take shape. There are many other instances where this distribution shows up, such as birth weights, the price of gas today at all the gas stations in the county, the amount of liquid in all the soda cans at the store, etc. This distribution is also linked to binomial probabilities.

Related links:

Wikipedia entry for Normal Distribution (gets fairly technical but you can read some of the basic details there)

simulation of a Galton Board (marbles bouncing down pegs on a board that we showed on the program)

The Cycloid

2008-04-30T20:21:00.000-07:00

A cycloid is the curve formed by a fixed point on the edge of a wheel as the wheel rotates along the ground. The curve is given by the parametric equations
x = r (t - sin t),
y = r (1 - cos t)
where r is the radius of the wheel. If you take one arch of the graph and turn it upside down it forms a ramp with a special property: it is the fastest path for a ball rolling down from one point to another. A second interesting fact: if you do have a ramp in this shape, no matter where you start a ball rolling, it will always take the same amount of time to reach the bottom. The cool photo is from illum on Flickr.

Note that our contest is still open!

Related links:

Wikipedia entry for cycloid

YouTube video of a marble rolling down a cycloid ramp

Contest!

2008-04-23T22:08:00.000-07:00

We have a new contest for you:

If you were to write the numbers 1, 2, 3, 4, ... up to 100,000, how many zeros would you write?

We received some incorrect answers during the program today (hint: the number of zeros is a lot higher than 11,000 or 11,111) so the contest is still open. If you figure it out, don't post an answer here! Be the first one to call us live next Wednesday to claim the prize. (1-888-762-1489 is the toll-free number.)

Hold That Water Back

2008-04-23T09:36:00.000-07:00

This week we looked how strong a dam must be to hold back the water in a lake.

It turns out that the force exerted on the dam doesn't depend on how much water is in the lake, but rather just on the depth of the water. It is tricky to calculate the total force on a dam however because the water pressure is different at different depths. So the bottom of the dam will experience a lot more force than the top. You can estimate the total force by considering horizontal sections of the dam separately, and if you want to be more accurate, calculus can get you to the precise value.

St. Louis Arch

2008-04-09T10:50:00.000-07:00

Today we looked at some of the mathematics of the Gateway Arch in St. Louis, Missouri. The shape of the arch follows an inverted catenary, a shape naturally formed by a hanging chain or cable. The monument was designed from an equation based on a hyperbolic cosine function.

Links for this week:

Wikipedia entry for the Gateway Arch

Wikipedia entry for a catenary

a square-wheeled bicycle

a YouTube video of a square-wheeled bicycle

Math Questions

2008-04-08T00:00:00.000-07:00

If you have a math question for us, leave us a comment here and we will try and help you out.

Feedback

2008-04-07T23:56:00.000-07:00

Do you have a comment for us regarding the program? Click "comments" below and type away!