This project was focused on finding the measurements of different shapes. We found the areas of different types of polygons, derived equations for the volumes of 3-D shapes, and then applied those to the real world by measuring anything we wanted.
In class, we did a series of worksheets which focused on finding measurements for 2-D and 3-D shapes. We started with the Pythagorean Theorem (a^2 + b^2 = c^2), which we used to derive the distance formula (d = √[ (x' - x)² + (y' - y)² ]). Then, we found the equation of a circle centered at the origin (x^2 +y^2 = r^2) which lead to exploring right triangle trigonometry (tangent, cosine, sine) and the unit circle (deriving the 45-45-90 and 30-60-90 triangles). That finished up length (1-D). so we moved on to ara (2-D) by examining different polygons, and eventually deriving the equation for the area of a circle. Then, we used our knowledge of area to solve for the volume of different 3-D shapes, by deriving that the volume is equal to the area of the base times the height and further proving volumes using Cavalieri's Principle. We primarily applied the Habits of a Mathematician Take Apart and Put Back Together, Start Small, and Look for Patterns.The final portion of this project was to take the different concepts we learned and to design a project that revolved around measuring anything we wanted.
Design Your Own Project
For this portion of the project, my partners and I chose to measure the volume of the Moon. This was definitely a challenging task, because it would be extremely difficult to obtain precise measurements by ourselves. However, we took inspiration from our initial idea, to use parallax to measure the distance to a star, and applied it to our current problem. Instead of using the angle an object travels across the sky in a 6-month period, as you do when using parallax, we used the field of view of a camera and a picture of a full moon. If you know the angle that the picture was taken with, and the distance from the camera to the object, you can figure out the length of the total image. Once we realized we could do that, we just had to figure out how much of the picture the Moon took up (in percentage) and we could easily get the diameter.
Overall, the project we designed went really well! The most difficult part was figuring out how exactly we were going to measure the Moon, but once we did everything went well. We had trouble in the beginning, our initial idea was to use the aforementioned parallax, but we quickly realized that obtaining the required measurements would be far too difficult, and so we came up with this idea.
Reflection
Overall, I found this unit to be quite enjoyable. Although I had learnt some of the material before, I was able to dive in deeper and see how each part built on the previous one and how they related to each other. We had to Start Small by deriving equations and solutions from past work, and we had to Take Apart and Put Back Together every problem to truly understand its relation to higher and lower level math. I really enjoyed the design your own project element at the end, especially because I got to work with Astronomy, one of my favorite subjects. Since our measuring was relatively accurate, I'm proud of our overall result.