Geometry Part II: The Sequel That's Better Than The Original

This week was all about delving deeper in to the different aspects of geometry.  While last week was mostly about becoming familiar with the different terms, this week we learned about transformations and got our hands dirty calculating angles of different polygons.  This week also introduced some new vocabulary as well.  My favorite new word:  Tessellate.  Here's a joke, Why was the number six afraid of tessellate?  Because tessellate nine!

Actually the definition of tessellation according to wikipedia is a "tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps."  That's fancy talk for the tiles you see in your bathroom or the designs in driveways or patios.  Of course it's more complicated then that and there are also different types of tessellations.  Regular tessellations are made up of congruent regular polygons of one type, all meeting edge to edge and vertex to vertex.

There are also semi-regular tessellations. These are formed by two or more regular polygons with the arrangement of the shapes the same at every vertices

Last but not least are the curved tessellations.  These are basically patterns of shapes that fit together to fill the given plane without leaving spaces.  The drawing below is from MC Escher called "Day and Night"

Tessellation is a great way to introduce the idea of thinking in patterns, which is an important factor in understanding mathematics.  Something that I always try to keep in mind when learning new aspects of mathematics is that I'm not just learning a new concept, but also a new way to think.  I think out of everything I've learned so far about mathematics is that the problem you're working on is second to the process.  Most people (including myself) forget the formulas and names of mathematicians, but it's hard to forget a thought process that is a part of every math lesson.  It becomes a way of life!