[Assignment 1: Doing Ancient Puzzles in Ancient and Modern Ways] Self-Reflection

 

             Our group’s goal of this project is to prove the formula for volume of pyramid (Volume=1/3 X Base X height) in both modern and ancient way. I received most of my education in Korea where learning and teaching by rote is the most common method. When I first got to know about the surface area and volume of the figure, my teacher just simply asked me to memorize the formula and taught me how to apply it to the formula to get the answer. I often stopped at memorizing formulas and focused on getting the answer right. However, this project made me realized the importance of learning mathematical history again.

             We first proved the formula in a modern way by splitting a cube into 6 congruent pyramids and 3 congruent oblique pyramids. As it was my first time to learn that a cube can be cut into 3 congruent oblique pyramids, it was not easy but fun to visualize it. Hence, we asked a class to make 3 congruent oblique pyramids that fit together to make a cube. I’ve also learned how ancients approached and solved the problem differently. Another thing that intrigued me was that the ancients used the concept of similar triangle that I learned in middle school to measure the height of pyramids. As similar triangles have the same shape but different size, the proportion of the corresponding sides are the same. Specifically, the ancients measured the height by using the shadow and the stick. And then, we investigated if this formula can be generalized into any rectangular prism by using a geometric method formulated in ancient China by Liu Hui. It was interesting to know that the concept of an infinite series is shown to prove the formula for volume of pyramids. I found it difficult to understand the process of a geometric method, at the same time; it was exciting to learn that there is totally new way to approach the problem.

             By looking far back into the mathematical history to find original proofs, I found this would be also useful when we introduce the new concepts to my future students. Proving virtually all concepts and formulas through a geometric approach beyond the algebraic approach is not an easy task since it requires a lot of time and effort for teachers to do so. However, I would like to draw my future students’ interest and help them understand clearly through more in-depth research on concepts rather than simply conducting class according to the curriculum.

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