New Math?

For the past few weeks the disappearance of flight 370 from Malaysia to China has been in the news daily. Earlier this week an announcement was made that there was certainty that the jet had gone down in the southern Indian Ocean. Even two days after that announcement, no physical evidence has been recovered. How could they have made that announcement with certainty?

Earlier this semester I used a Performance Task that I created for use in grade 6 to teach my students about how the GPS locating system works. A key element of the system is triangulation. Essentially, if three distances to a given location are known, the location can be identified with certainty. Think of it this way: If you know only one distance, the location can be anywhere on a circle with that distance as the radius. If you know two distances, the location is one of the two specific locations where the two circles cross. If you know three distances, the location has to be the only spot where all three circles cross. (If you can’t picture this, draw the circles.) This process of finding a location is known as triangulation.

With the Malaysian flight, they were telling us for several days that the flight was known to have gone on either a northern route or a southern route. Evidently they had two signals that were being used to calculate distances, and they had two points of possible location (two intersecting circles). At any one moment, they knew the plane was either at this particular point on the northern route or this particular point on the southern route. Since they were unable to rule out one or the other route, they evidently did not have three sources of data – they were unable to triangulate.

But then, suddenly, they were able to rule out the northern route. What happened? How did they suddenly find a third source of data in order to use triangulation to become certain about the southern route? Apparently someone at the British satellite data outfit had a brilliant insight that the Doppler Effect would cause the signals that they did have from the plane to look different if the plane had been on the northern route vs the southern route. (Without going into all the physics of it, the Doppler Effect is what causes a moving vehicle to sound like it has a higher and higher pitch as it approaches you and then a lower and lower pitch as it moves past and away from you. The movement of the object distorts the sound waves a bit.) As I understand this story, it sounds like this technique had never been used before to deduce location. It sounds to me like it was an entirely new insight into how to use existing science, math, and technology.

The fascinating thing is that the authorities were willing to make their announcement based on the mathematical certainty that was available, even without physical evidence. The search teams were able to focus their resources on a much smaller (but still huge) area. Just this morning it seems that they may have located several objects that may have come from the jet. We still don’t know, but it looks promising.

And people wonder why they need to know math.

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