Geometry
This is my geometry page! I have this class first period, and my teacher is Cathy Eagan. In her class we do everything from basic algebra to things I truly wont learn until next year in Algebra 2. Below is a list of things we have learned so far in her class.
1st Semester Topics
- Inductive/ Deductive Reasoning
- Recognizing number patterns and modeling them with an equation
- Seeing special angle relationships
- Finding points of concurrency of triangles
- Creating constructions with a compass and straight edge.
Exploration The Seven Bridges of KoenigsbergFor homework one day we had to explore different patterns that were made up by this man named Euler. We had to determine whether or not the patterns were created by him. There were 11 patterned shapes, and it took about 45 minutes to complete, well for me anyways! It was fun, but quiet difficult, because we had to see if the patterns met up at the same start place or if they ended up somewhere else. The trick to the patterns is where the angles meet, you count how many angles come from the lines that intersect. If it mostly has odd numbers, then it is a Euler.
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POW (problem of the week)This semester we completed many different POW's, and one of my favorite ones was the Path Finder problem. It was where we had to find a certain amount of paths on a 4x4 or 5x5 grid. This helped me understand the more advanced equations that we were using to solve the other answers. It was entertaining because I had to keep going back over it, again and again, because I had accidentally forgot or repeated one of the patterns.
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"The mathematician does not study pure mathematics because it s useful; he studies it because he delights in it and he delights in it because it is beautiful." ~ J.H. Poincaré
I believe this is true, mathematics is beautiful. It is an art form, in my opinion, a very advanced, complicated art form. It makes me think about how much I love art, and how I should appreciate mathematics for what it is, instead of thinking "UGH, math is HARD!". And it also makes me think about how I should keep practicing to keep getting better, just like with art. So whenever Cathy says that "Math is Beautiful" I should cheer her on, because it is beautiful, although difficult. I find that equations are so beautiful, the lettering and the writing, how it looks so difficult, but after you learn it it becomes so obviously easier for you. That's what I love about Math.
Tessellation ProjectWe have just gotten finished creating a tessellation to show how patterns and shapes can be fitted just so, so that they can create a repeating pattern. This took a while for me to figure out, because I wanted to do many different shapes and patterns. In the end I stuck with a cloud pattern with a rainbow in the center.
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Slice Form Project
For one of our last projects in Geometry, we did a really cool design form. It is called a slice form. It is where you take paper and cut it into different shapes that correspond with one another, so that they will create a 3-Dimensional figure. We had to create a write up to go along with it, click here to see it.
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Final Project
For our end of the year project, we had to come up with a creative piece and an instructional piece about something we learned in class this year. I decided to create a new tessellation and a poem about patterns in geometry. It is a Shakespearean Sonnet, which means it has a specific pattern and syllabic pattern.
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pattern: abab cdcd efef gg
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