TsáKtalay’pa and I tackled the proof of the formula for volume of a pyramid: V=1/3*base area*height, in ancient and modern ways. The original problem suggests investigating through two special cases, dividing a cube into six congruent symmetrical pyramids, and dividing it into three congruent oblique pyramids. We argued that the Ancient Egyptians likely derived the formula not from geometric dissections of a cube but through practical building methods. They likely began with a frustum for structural stability and efficiency of materials, and continued building upward to form a complete pyramid, perhaps aiming to connect with the stars. For the modern proof, the intuitions from these cases were helpful. We provided clay models for our classmates to explore the two divisions of the cube, along with paper templates to visualize the second case of three asymmetrical pyramids. We extended the discussion by introducing the Mayan pyramid, El Castillo, which resembles stacked square prisms and provided intuition for the formal proof using integration. This comparative approach enriched our understanding of the formula, blending practical, historical, and mathematical perspectives.
I learned a lot from both the process and content of this presentation. It sparked my curiosity about formulas I had previously taken for granted. Taking the time to explore and question them helped strengthen my relational understanding and appreciation of math, making me feel more prepared as a future math teacher. Understanding these concepts through ancient methods added historical context and narrative to the formulas, enriching the learning experience. I especially enjoyed the "extension" part of the presentation—not only was the research helpful, but it also encouraged me to connect and expand on different areas of my knowledge.
It was also really inspiring to see my classmates' presentations. I learned a great deal from this project, and I plan to adapt it into a class activity in the future.
Great work, Jasmine!
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