Final Examination

III. Past Discussions

IIIa.

As I have not had geometry since high-school, using Geometer SketchPad to examine
constructions was a wonderful learning experience. The write up in which I learned the
most was the Pedal Triangle write-up. This examination caused me to examine the
relationships between different aspects of triangles. This reinforced what I had
previously learned within the GSP write-ups and caused me to re-examine the relationships
among points that can be constructed for triangles. During this write-up, I became more familiar with the definitions of the points and circles that can be constructed for a triangle. I had previously learned what they were, but this write-up seemed to cement their relationships together.

IIIb.

I am the most satisified with the write up about a triangle and its circles. This topic of this write up was very straight forward. After constructing all the circles for a given triangle, it was easy to examine what happened to the circles as the triangle was adjusted. The results were very consistent from one triangle to the next. There were no hidden surprises as the type of triangle was changed. This write-up also helped to solidify my understanding of the geometry of triangles.

IIIc.

My most useful effort was on write up #2 , #3 and the first section of the final. I have
previously taught and continue to teach primarily Algebra I and II. By examining conic
sections in a graphical manner, I became aware of new relationships between the
different types conic sections. I believe that the most useful was the examination of quadratic equations in write-up 2.

The previous equation, when a is varied, shows relationship that exists between a circle, ellipse, line and hyperbola. This examination opened new doors to the way that I can present conic sections to my students. Rather than primarily focusing on the differences between the equations of a conic section, similiarites should be stressed as well because they are all related.

IIId.

When I was examining parametric equations, before I wrote up the cycloid, I examined many parametric plots. I was intrigued enough by their relationships to go back to my old textbooks, and get other textbooks from my friends, to examine parametric equations in more detail. I spent many hours examining the relationship between x=cos(at), y=sin(bt) and their graph. This was one of the write-ups that I actually enjoyed researching and forming opinions about. It has been many years since I reseasrched topics in math because I wanted to. This write-up removed math from only being a job, and once again awakened my interest in math.

I Hyperbola and Box Maximization

II A New Look

III Past Discussions