Pi in the Sky

Pi In The Sky (PITS) consists of a loose collection of virtual globe (VG) activities with a slight mathematical twist, wherein students search for interesting circular structures on the surface of Earth (Moon or other planets) and measure the circumference C and diameter D of each structure, using the built-in VG measure tool, in order to determine experimental values of pi from the C/D ratios. Examples of man-made circular structures visible using VG browsers include Fermilab and l"Arc de Triomphe roundabout; quasi-circular natural structures include certain volcano calderas and impact craters. Since a circle is but a special case of an ellipse, a natural extension of the activity involves making similar measurements of perimeter P, semi-major axis a, and semi-minor axis b of a visible elliptical structure (such as one of the thousands of elliptical Carolina bays, enigmatic depressions on the Atlantic Coast of North America) and solving for pi using Ramanujan's first approximation for the dependence of the perimeter of an ellipse on a and b. PITS exercises can be adapted to a wide range of student ages and teaching goals. For instance, K-6 students could measure C and D of the huge irrigation circles near Circle, Texas, to discover pi in the same way they might infer pi from measurements of coffee-can lids in math class. Middle school and high school students could move beyond man-made circles to consider the near-circularity of certain volcano calderas and impact craters in earth science units, make measurements for Olympus Mons on Mars or Crater Kepler on the moon in astronomy units, or search for circularity among Arctic thermokarst lakes as an introduction to climate change in tundra environments in environmental science units; such studies might ignite student curiosity about planetary processes. High school students of analytic geometry could examine several elliptical Carolina bays and calculate not only values of pi (as noted above) but also determine the range of eccentricities exhibited by these structures; through these exercises, ellipses acquire significance beyond conic sections and planetary orbits. At whatever level, PITS exercises function as easy bait, enticing students to learn to operate VG software and make observations and quantitative measurements of interesting Earth features. On a deeper level, these exercises provide a context and tool enabling VG explorers to fly above Earth's surface, to see this surface megascopically as it heretofore has never been seen, and to play in the metaphorical geometric intertidal zone that resides between shallow, eyes-on-the-ground, normal perception and the deep-blue depths of the cosmos.