Choose Your Own Project!
Or should I say Create Your Own Project? For the very last math project of our Sophomore year, our teacher decided to let us do a project of our choice. She gave us options (all of which were fun and artsy) but also let us suggest a different project idea of we had one! We then worked on these projects in groups, creating deadlines and requirements for ourselves, to produce beautiful work and an amazing understanding of math.
My Project
Personally, I decided to create a completely different project of my own! In the previous year, I had done a project where we learned Geometric Constructions. These are basically work of art consisting of perfect shapes and lines. Here's the trick though, the only tools used are a pencil, straight edge (not a ruler), and a compass. Using these tools, we had to "construct" a pattern of some sort with perfect shapes. Well, geometry has never been my strong (haha, get it, Strong?) suit so I had, for some reason, a lot of trouble wrapping my mind about this fairly simple concept and I had a lot of trouble (okay, part of it was trouble using the compass but, you know..). So, when we were given the option of creating our own project, I thought back at that time the year before and jumped on the opportunity to re-do it so I can, not only better understand the concept, but to add even more to the knowledge required (maybe make some discoveries on my own). Thus, the project was born.
The Process
I began, and spent some time, trying to think of what the image I was going to create would look like. This is crucial because it determines the whole rest of the project and my learning. I didn't want to create just a regular pattern, I wanted something that would be a little more of a challenge. I thought and thought and had several interesting ideas (such as creating a faerie, scenery, abstract, etc..) but neither of them I liked thoroughly until I thought of a dream catcher. I really lied this idea of using constructions to create the dream catcher pattern and then being able to embellish the exterior so I began. I looked online for some dream catcher designs I might want to do and decided on this one:
I liked the idea of the starbursts and decided I could construct them by putting triangles along the rim of a circle. I decided on some small variations but this was the basic idea. I then spent a lot of time planning and learning/practicing the construction(s). Below is the rough draft I created of the unfinished picture:
As I created this, I wrote down my steps so I'd be able to remember them for the final. These are as follows:
- Draw a circle the size of 2/3 of the page to start
- Create 3 perpendicular lines bisecting the radius line into fourths (bisect the radius 3 times).
- Draw 3 circles whose centrepoint is the centre of the big circle and whose radii rest on the bisector lines.
- Draw a horizontal line across the centre of the image (I had to cheat a little doing this by lining the traight edge's edge with the side of the paper)
- Draw a perpendicular bisector of that line.
- Bisect all four of the 90 degree angles.
- Bisect each 45 degree angle
- Using the distance between all the bisecting lines as the side lengths, draw 16 triangles bordering the edge of the third largest triangle.
That is as far as I got for my rough draft since I was anxious to move on but, in my head the rest of the construction was planned. Or so I thought. I began on the final and it was going well. I was taking great care to plan each move and not mess up in the beginning which was great. After a while, though, this died down which was not good. About 2/3 of the way through, I started to get real confused. The lines were messing with my brain or something and I forgot how the image looked on my rough draft. I ended up drawing the amount of triangles on the inner circle that I was going to draw on the outer circle. I realized this as soon as I finished drawing them but, being pressed for time, I decided I'd just have to move on. I thought, "Okay, this is going to be different. I will have double the amount of triangles on the inside than on the outside...". So I did that. After all the triangles were finally constructed, I stepped back and looked at the image. It was really cool. Believe it or not, but all the lines I had made the image look neat. Especially in the centre. I decided then (partly because of it looking cool and partly because of the time) that I would leave the rim of the innermost circle blank and just trace the lines inside that circle with colour and then drew feathers and beads to hang from the dream catcher. I did just this and this is how it looked:
Cool right? So, after this, I traced all the triangles (not the base lines) with coloured pencil and erased the extra lines. Then, just for the hell of it, I added mini circles in between the big triangles. I also coloured the feathers and beads. Below is the final product!
I signed this and gave it to Mrs. Strong as a gift since I will miss her next year! c:<3
Reflection
I am overall very glad I did this project to refresh my mind on the topic. I definitely feel a lot better about my understanding of the constructions. I am a little disappointed that I made mistakes on the final image but, in the end it turned out fine. Looking back, I could have used the same lines for the outer triangles as I did for the inner ones and it would have exactly matched the image this was based off of (and I would have time after that to add more, such as petals which I originally had the idea for) and I have no idea why I didn't think of that but, what's done is done. The project was still very fun and I looked forward each time to working on it! My teacher was also very supportive during the time since I had a lot of questions (especially in the beginning) which is really good!