Rubber Sheet Geometry

    What if, instead of paper sheets, we used rubber sheets to write and draw on?  With advances in computer technologies, we really do not need to imagine this thought at all.  For example, inspect the picture below.

    If someone were to grab the right and left hand sides of this picture and pull, notice how the image distorts from its original state.

    Now, let's squash the poor fish.

    Keep in mind that we do not want to tear this image, we just want to distort it.  One could easily argue, and be correct that the images above are different in many ways, but the fact remains that they still are fish!

    An entire branch of mathematics is devoted to the ideas mentioned above, and is called Topology.  Topology deals with the ways that surfaces can be twisted, bent, pulled, or otherwise deformed from one shape to another.  A topologist is interested in the properties that remain unchanged after all these transformations have taken place.

A new way of looking at things...