Tuesday, November 24, 2015

Topologist's Map of the United States

To a topologist, two shapes are "the same" if one can be stretched, twisted, and distorted into the other shape without breaking or tearing it.  Shape, angle, size, distance, and position can be completely different, and yet the two shapes are topologically equivalent.

This is a topologist's map of the 48 contiguous United States.  While the states are not recognizable, you can work out which is which by how the states are connected to each other.  For example, which is the only state that borders exactly one state?  Can you find it on the topologist's map?  Can you identify all the states?  (One note:  Lake Michigan is included as one of the polygons, and the state of Michigan is represented as a single polygon, which was necessary to avoid some strange results.  So all together there are 49 polygons here.)

For a printable version click here.

For the solution, click here.