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Why December 21 Is the Longest Day of the Year
by Stan Wagon (Macalester College)This article originally appeared in:
Subject classification(s): Mathematical Physics | Applied Mathematics | Differentiation | Single Variable Calculus | Calculus | Trigonometry | Spheres | Solid Geometry | Plane Geometry | Geometry and Topology
Applicable Course(s): 4.18 Applied Math (Math Modeling) | 4.9 Geometry | 3.1 Mainstream Calculus I
This article is part of the Mathematics of Planet Earth 2013 Collection. An equally accurate title would be why the day of latest sunrise and the day of earliest sunset do not occur together and neither occurs on the shortest day of the year. Using simple geometry, trigonometry, and elementary calculus, the author describes the graphs of solar noon (at 44 degrees north latitude, i.e., at St. Paul, MN) and the graph of its derivative, the solar day and uses them to explain the sunrise and sunset times.
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