This year I'm taking the wonderful course of Geometry. Here you can see all of the projects I've done in this class.
SEMESTER ONE
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and delights in it because it is beautiful." --J.H. Poincare
Here are some topics we’ve hit this first semester:
1.
Inductive and Deductive Reasoning in Geometry
Inductive: Inductive reasoning is when a conclusion is reached
from the information of specific facts
Deductive: Deductive reasoning is used by making general
conclusions by using all known ‘smaller’ facts
2.
Recognizing Patterns and Modeling them with
Equations
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3.
Special Angle Relationships
4.
Points of Concurrency of Triangles
5.
Constructions (Using Compass and Straightedge)
6.
Discovering and Proving Triangle Properties
7.
Discovering and Proving Polygon Properties
I really enjoyed doing constructions in Geometry. I enjoyed
this because I like art and drawing, and it was kind of neat to be able to
prove that your construction was 90 degrees without using tools besides a
compass and straightedge. Here’s a photo of a pair of parallel lines I
constructed.
Two years ago, I would have responded to J.H. Poincare’s quote
(found above) by probably saying it was the worst quote in all history. Maybe I’m
still not quite ready to say that I ‘delight’ in math yet, but this year I’ve
started to see the beauty in it, especially when we learned about symmetry. You
can see by the picture of fish above (that isn’t perfectly symmetrical, but is
close) that many math and symmetry concepts are used in art to create visual
balance. I find this very relevant and beautiful.
Here’s an example chapter composition book review:
