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Morgan O’Hanlon
Pre-AP Precalculus Pr. 5
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05/01/14
Analytical Report
The author Orson Wells once said “There are only two emotions in a plane: Boredom and
terror.” However, this statement is proved false with the consideration of the complex
mathematical issue of polar graphs and coordinates. These graphs are used by air traffic
controllers to guide thousands of planes daily through the skies.The work that these professionals
do behind the scenes of each flight is fascinating due to their scrupulous evaluation of the
movement of planes and the value that they have concerning the safety of one billion people
annually (Neal). The mathumentary that our team created aims to engage next year’s PreCalculus
students in the high stakes are placed on air traffic controllers’ ability to assess these graphs
accurately.
Our film production has evolved greatly throughout the production process. Some
difficulties we encountered include initial formatting difficulties with the flow of our script,
finding content that was both an accurate assessment our knowledge of polar graphs while
remaining accessible to entry-level viewers, and engaging our audience in the topic at hand. We
dealt with these issues by rewriting our script omitting cliché introductions and incorporating
mathematical elements throughout the mathumentary, rather than being condensed. Despite these
changes our production team was able to make our topic engaging to the audience by
incorporating the plane crash context between every application of math. We were most
successful at slowly building understanding of our topic: first with a mini-lesson on graphing and
then with application of graphing in the plane crash scenario. Our video as a whole was cohesive
and engaging due to the use of dramatizations of the collision and the placement of the smart
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board in the main frames. The smart board was a key element to our presentation because it
better allowed us to demonstrate and explain our work.
The Überlingen mid-air collision occurred on July 1, 2002 at approximately 9:35 P.M.
over Überlingen, Germany. The two planes that collided were a Boeing B757-200 and a Tupolev
TU154M. The Boeing was a cargo plane headed from Italy to Belgium with 2 crew members;
the Tupolev was a passenger jet carrying 9 crew members and 60 passengers. All 71 people
involved in the crash were killed. The air traffic controller at Zurich on duty at time of the crash
was Peter Nielsen. At the time of the crash, his equipment was malfunctioning and was
monitoring multiple screens simultaneously. Despite efforts made by Nielsen to tell the plane to
“descend” and the jet to “climb” confusion by both crews led to the ultimate destruction of the
planes (Germany).
The concept of Polar graphing is foreign to the Algebra Two students. In order to get
them acquainted with the concept, a section of our mathumentary is devoted to familiarizing
them with this concept though comparison of graphing on a rectangular coordinate grid with
graphing on a polar coordinate grid. After their basic knowledge is established, we show the
audience the graph to the left, which shows the projected paths of the two planes ( blue the
passenger jet and red as the cargo plane). The paths of the planes are each rays spanning the
diameter of the graph due to their straight paths of travel. The two paths meet at the pole of the
graph, which represents the point of collision. In the Überlingen mid-air collision, the passenger
jet hit the cargo plane at an angle of 90 degrees traveling at a bearing of 94 degrees with a speed
of 235.1067 meters per second; the cargo plane was traveling at a bearing of 184 degrees with a
speed of 261.338 meters per second (Germany). The coordinate points on the graph of each path
before the plane crash can expressed as (r, 266 degrees) and (r, 176 degrees) with r being any
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positive real value; the points of the crash are different from their bearings because there are no
more points to plot after the plane crashes at
the origin and the cargo jet and passenger
plane were traveling from the south and east,
respectively.
Polar Graphs and coordinates are
applicable to society in a way that affects
people worldwide and AGS students in
particular when they travel on planes on trips to places such as to Costa Rica, Boston, and
Turkey. This method of graphing ensures the safety of all those who travel by air, therefore,
precision and competence in the mathematics behind air traffic controlling is of the utmost
importance in order to prevent avoidable disasters and save lives.
Works Cited
Germany. Federal Bureau of Aircraft Accidents. Uberlingen Investigation Report. By Uwe
Berndt, Jens Friedemann, Hans W. Hempelmann, Eberhard Krupper, Heinrich H.
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Niebaum, Hans Peters, Johann Rueb, Dieter Ritschel, Karsten Serverin, Frank Stahlkopf,
and Axel Thiel. N.p.: n.p., n.d. Web. 27 Apr. 2014.
Neal, Karla V., R. David Gustafson, and Jeffrey D. Hughes. "Polar Coordinates; Vectors.”
Precalculus. N.p.: Cengage Learning, 2012. N. pag. Print.