Measuring Your World Project
Project Overview
This project began by taking a look at basic trigonometry, with concepts such as the sine, cosine, and tangent ratios and the unit circle. We also took a look at the distance formula and how it can be derived, and the equation of a circle. Later, we explored deep into the area and volume of shapes such as circles, triangles, prisms, and spheres, and eventually decided on an object from our world and calculated its volume.
Design Your Own Project Writeup
For the Design Your Own Project portion of this project, we were told to choose an object and calculate its area. I chose my three ring binder, because I thought it would be enough of a challenge to be interesting, but not too difficult for me to solve within the time I had.
To start, I thought of all the different shapes I would have to measure and how their volumes could be calculated. I then drew diagrams and measured the pieces so I had a better understanding of the shape I was figuring out. Once I had all those measurements, I started adding them together:
V(Binder) = V(Plastic base) + V(Ring Base) + 3 * V(Ring) + V(Clip Slot) + V(Clip)
Where “Ring Base” is the metal strip inside that the three rings are attached to, “Clip” is the plastic button clip that opens the rings, and “Clip Slot” is the small metal piece with a hinge for the clip on the inside. Plugging in the numbers gave me this:
V(Binder) = 32.9733 + 1.4598 + 0.1566 + 0.0292 + 0.0669 = 34.6858 cubic inches
Reflection
I really enjoyed this project and the content we covered. My favorite part was the “Design Your Own Project” part, but that’s also the one I could have improved on the most. I didn’t spend as much time on that portion as I’d hoped, and I did most of the work the day before it was due, even though we had a week. However, I still think I did well with Habits of a Mathematician, such as “taking apart and putting back together” and “being systematic”. At first, I knew that the only way I could find the volume of my binder would be to split it into easy to measure parts. Then, I created a systematic approach to measuring the shapes by creating a tree diagram full of all the measurements and calculations I needed to make.