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Classroom Capsules and Notes
Mathematics of Planet Earth 2013 Collection
Welcome to the Mathematics of Planet Earth 2013 Collection assembled from the print journals of the MAA: American Mathematical Monthly, Mathematics Magazine, and College Mathematics Journal. The collection contains 16 articles, all related to the Mathematics of Planet Earth 2013 theme. Each article has a page with a summary of the article, publication information, and a link to a PDF copy of the article itself.
We begin with an article written by Phillip Griffiths and published as the lead article in the American Mathematical Monthly for the January 2000 issue: " Mathematics at the Turn of the Millennium." In this article Griffiths looks back over the history of mathematics with particular emphasis on the last century and then outlines some of the mathematical challenges for the new century.
Two articles deal directly with the sun and our planet: "Early Sundials and the Discovery of the Conic Sections" by W. W. Dolan and "Why December 21 Is the Longest Day of the Year" by Stan Wagon. Also following the astronomical theme, we have an article by Marc Frantz on locating the position on an object in space travelling around another in an elliptical orbit: "Some Graphical Solutions of the Kepler Problem."
We have two related articles about a mathematical explanation for the Tacoma Narrows Bridge collapse in 1940: "Large Torsional Oscillations in Suspension Bridges Revisited, Fixing an Old Approximation" by P. J. McKenna, and an article written by McKenna and his student Cillian Ó Tuama, "Large Torsional Oscillations in Suspension Bridges Visited Again: Vertical Forcing Creates Torsional Response."
Two articles in the collection deal with relativity: "Rearing Its Ugly Head: The Cosmological Constant and Newton's Greatest Blunder" by Hieu D. Nguyen and "The Clock Paradox In Relativity Theory" by Alfred Schild.
The oldest article in the collection describes the teaching of meteorology to soldiers during the World War II: "The Applications of Mathematics in Meteorology" by B. Haurwitz. In a 2007 article Katherine Socha discusses water waves, starting from a fascinating picture taken during the same war in "Circles in Circles: Creating a Mathematical Model of Surface Water Waves." Also on the theme of waves in water, Cathleen Morawetz writes about the transmission of whale sounds over long distances in "Geometrical Optics and the Singing of Whales."
Lyle Long and Howard Weiss discuss the question of whether reaching terminal velocity could have contributed to the survival of a 102-year-old woman in a fall from a fourth floor window in "How Terminal is Terminal Velocity?".
David Smith examines world population growth models in the 1977 paper, "Human Population Growth: Stability or Explosion?". The data are somewhat old, but the models and issues are still relevant.
Two articles in the collection concern navigation. In "An Application of Geography to Mathematics: History of the Integral of the Secant," Frederick Rickey and Philip Tuchinsky examine the map developed by Mercator and the accompanying need to be able to integrate (sec heta). In "Global Positioning System: The Mathematics of GPS Receivers," Richard Thompson gives a nice two-dimensional example to illustrate the ideas behind the global positioning system.
The final article in the collection was composed by a team of high school students in connection with a modeling contest. The article, "Ethanol: Not All It Seems To Be," written by the team of Thomas Jackson, Kelly Roache, Afanasiy Yermakov, and Jason Zukus with team advisor R. Eng, points out the problems with replacing 10% of the gasoline used in 2008 with ethanol.