Understanding the landscape of a two-dimensional world has a variety of uses and insights.  But it is the three-dimensional world where we experience all of our real-life encounters, where geometry really springs into a vivid existence.  Every object has a shape, many of which are easily recognizable as a geometric entity that lends itself to a mathematical rendering.
     Cans and bottles are oftentimes circular cylinders, most boxes are usually rectangular prisms, balls and astronomical bodies are typically spherical, etc.  So, now we forge ahead into the truly everyday domain of the physical world which we navigate our lives amidst, probably with little regard for the mathematical infrastructure that underlies the fabric of it all.