Throughout the course, it has been both exciting and challenging to solve typical mathematical problems- such as long division- using Babylonian and Egyptian methods. It was especially rewarding to apply Egyptian multiplication and decipher Babylonian symbols, exploring how these techniques were used by ancient civilizations.
Initially, I was a bit apprehensive about this assignment. I knew my instinct would be to approach the problem using modern algebraic notation and formulas that are deeply rooted in my mathematical and geometric foundations. However, as my group began working through the pyramid task- starting with part (a), where we had to draw four spatial diagonals- we realized we could use a method of dissection to create six congruent, square-based, perpendicular pyramids.
We began by discussing the volume of the cube, which naturally led us into a back-and-forth conversation about how that related to the volume of a pyramid. Admittedly, we already knew the "end goal"—the formula for the volume of a pyramid- so that gave us some guidance as we worked backward from the cube to derive the relationship.
In part (b), Yuki drew the oblique pyramids while Shannon created impressive 3D models, which greatly enhanced my understanding. We noticed that the method of “zeroing” the base was a recurring theme in the process, and we became curious about how and why the Egyptians arrived at this concept. An earlier group- Ross, Danielle, and Jayden- had derived the formula for the volume of a truncated pyramid using similar quadratic reasoning, and their work closely mirrored the thinking we used for the full pyramid volume. Their presentation helped deepen my understanding and sparked thoughts about further mathematical extensions, including calculus-based integration and the role of “b” as the top edge in the pyramid’s triangular cross-section.
After their presentation, I really wanted to understand why, in the full pyramid volume formula, the “b” value is simply zeroed out. The textbook explained that in a full pyramid, the top surface area present in a truncated pyramid no longer exists, which seemed to hint at the concept of a limit. As a result, the “b” value is omitted in the full pyramid formula.
Learning from other groups' presentations- especially the geometric dissection problems with Ross, Danielle, and Jayden- was incredibly engaging. Danielle’s 3D model and Shannon’s 3D visualizations stood out to me, making it clear how effective physical models can be in supporting geometric understanding. This experience has made me realize how much I want to incorporate 3D models into my own teaching of volume and surface area. It reinforced the value of hands-on manipulatives and how they can make abstract geometric concepts more tangible and meaningful.
