Monday, October 10, 2011


"Obvious is the most dangerous word in mathematics."
                -- E. T. Bell

In the last chapter we were introduced to the concept of betweenness of points, which is maybe the first time so far that we've smacked our collective foreheads and said, "No kidding. Do we really have to waste our time defining this idea that's so totally obvious?"  On some level, this is a legitimate complaint.  I mean, we can look at a line segment with P and R as its endpoints and immediately understand that every other point on the segment is between those two.  This picture completely jibes with our everyday understanding of what it means for a thing to be between two other things.  And in that world, betweenness doesn't seem confusing in the least.  You know that your C- in Geometry is somewhere between an F and an A (or between a D and an B, for that matter).  You know that my classroom is between Mrs. Brown's and Miss Forsberg's (and so is Mrs. Wavrunek's).  And you know that the Vikings are somewhere between awful and terrible.  These are facts.