Thursday, December 8, 2011

Welcome!

Hello!  Welcome to my Geometry page!  Let's start with an explanation of Geometry, shall we?  Geometry is the math of shapes: polygons, lines, angles, etc.  Geometry is used to build and measure and help improve our deductive and inductive reasoning skills among many other things.

   Now math and I have a very complicated history.  First, I absolutely adored it.  I liked finding the patterns in the numbers and exploring it.  Then it became increasingly difficult.  Because of my pride and a lack of enthusiasm for my teacher I wouldn't go to get help, so I began to understand less and less and began to be really frustrated with math and my grades altogether.  Then I came to Animas.  I started in Algebra two and earned the best math grades I'd earned in years, because I was actually understanding it!  I'm hoping ot continue this trend throughout the rest of this year as well, because math really is enjoyable if you just know what you're doing.

  
   One of my favorite topics to study was triangles.  This was a very broad topic and we studied many ways of finding the measures of angles and such through the use of triangles.  By adding up two interior angles of a triangle, you can get the exterior angle of a triangle.  The exterior is the supplementary line that extends from one side of a triangle, creating an angle outside of the triangle, like so:

Z is the exterior angle.  Now the interior angle is supplementary, meaning that
Z+the interior angle= 180 degrees.  So, if you subrtact Z from 180, you'll get the measure of the interior angle.

POW!  Problem of the week:

What just is a problem of the week?  Once a week, usually on Monday, Cathy hands out little problems that we have the whole week to solve.  It is often very closely connected to the content that we are learning that week, and they are always interesting.  For instance: Did you know that you can prove that a triangle's angles can add up to 180 degrees with a pencil and without making a single mark on the paper?  Lay the pencil along the base of the triangle and make a note of the direction it is facing.  Turn your pencil so it's facing backwards and is lined up along one of the sides.  Repeat this process for the next side but so it's facing forward.  do it again.  Which direction is your pencil facing?  If it wasn't a 180 degree turn, then maybe you're turning too much...

A Quote to Ponder:

J.H. Poincare (1854-1912), (cited in H.E. Huntley, The Divine Proportion, Dover, 1970)

"The mathematition does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful."

My Reaction to Said Quote:

   Anyone who knows me, knows me for my writing, or my drawing, not my mathematics skills.  I'm one who created things, whole new worlds for the sake of creating them and the freedom that I have in the creation.  By eighth grade I had pretty much decided that I would absolutely never go into a field requiring more than very basic problems because I honestly didn't feel smart enough to be in one of those fields.  It limits me a lot.  In class now though I do enjoy solving the problems.  Because each one has an answer and those answers make sense as long as you know the pattern.  Each of those patterns are discovery as well, and their own creations.  So yes, I can definitely see a beauty in Geometry that I haven't seen in math for a really long time!

Well, if you made it all the way through, thanks so much!  Night!