Tuesday, January 28, 2014

Mapping the U.S.A. (with Oblique Triangles)

I have seniors these days and we're doing Precal. The students learned in Geometry that any three side lengths will determine a unique triangle (as long as the sides obey the Triangle Inequality): lengths of 24, 9, and 30, for example, can only be fit together in one way to create a triangle. Only later, however, do they learn about the Law of Cosines, which allows you to find the angles of that particular triangle. So starting from “side side side” information, they can calculate an angle, then use a protractor to draw the triangle accurately. It occurred to me that we could create a map by drawing triangles in this way. If the students looked up their own three cities and/or towns, and the distances among those places, they could make their own triangular scale map- and if they all used the same scale, we could fit their maps together.

The restrictions I gave them were:
-the scale is 1 mm = 1 mile.
-the distances cannot exceed 300 miles on any side of a triangle.
-the places must be within the 48 states.

Here’s how it’s looking overall right now. You can actually see the country taking shape.