Web-based Practice
The Great Circle by NLVM
Course, Subject
Geometry (Next Generation), Math, Science & Technology, Mathematics (NYS P-12 Next Generation)
Virtual Manipulative
Click here for this interactive resource.
Description
This virtual manipulative can be used in place of a physical globe, but ideally it should be explored while students have access to a globe of the world. We are so used to seeing flat representations of world maps that it may be counterintuitive that the shortest air route from San Francisco to Moscow goes almost over the North Pole, not over Chicago.
With this Great Circle manipulative, when the student clicks San Francisco and then Moscow, the great circle route is shown in green and the straight-line path on the Mercator map of the world is shown in red at the bottom of the manipulative, and also on the globe at the top. By rotating the virtual globe, it should be apparent how much shorter the green great circle route is, but this observation has even more impact if students have access to a physical globe, where a string can be stretched from one city to the other. The stretched string is automatically part of a great circle. From this kind of exercise, students should be able to recognize that great circle distances are always the shortest and that a great circle is what we would get by slicing a plane through the center of the sphere and the two cities on the surface.
While we do not have any cities on our globe that are at opposite ends of a diameter of the sphere, students should discuss what the shortest path should be in that case. Is the shortest path unique in such a situation? Look for some such pairs on a globe, as for instance, two locations on the equator.
Content Provider
The National Library of Virtual Manipulatives is a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis). The project includes dissemination and extensive internal and external evaluation. For more information, please visit http://nlvm.usu.edu/en/nav/vlibrary.html.
Credits
Principal Investigators
Larry Cannon
Jim Dorward
Bob Heal
Leo Edwards
Java Applet Programming
Ethy Cannon
Joel Duffin
David Stowell
Zeke Susman
Richard Wellman
Jennifer Youngberg
Web Site Programming
Joel Duffin
