Reflection on Assignment 1

 In this assignment, my groupmates and I worked on reconstructing the Egyptian approximation formula for a circular. As seen in the figure below, it is intuitive to conclude the inscribe circle in a square with side length d is (7/9*d)^2. However, it is different than the Egyptian way of approximating it (just by a little) – (8/9*d)^2. It is not until we use Babylonian’s way of approximating square root then we figured out. As an extension, we wanted to approximate the volume of a sphere inscribed in a cube. At first we found our approximation pretty off, as we just trimmed off the canners of the cube. We then tried a more complicated way of trimming the cube to obtained a much more accurate approximation of the volume of the sphere. We also dig deeper into other hypothesises on how the Egyptian came up with the “formula” of A = (8/9*d)^2. I personally really enjoy taking a simple topic, at least in modern day standard, and explore the sophisticate nature of it. In this case it is the area of a circle. Looking back at the process of us preparing for this presentation, I have two main takeaways from it, which I will discuss further below.

 

From the reading, we realized that Babylonian were able to approximate square roots by using root(n)=root(a^2+/-r) which is around a+/-(r/2a). While we worked on our extension, we wanted to come up with a similar approximation for cube root of n. After working on it for a while, a groupmate of mine realized what the Babylonian approximation is just what we called linear approximation today. This amazed me that a first-year calculus topic was used thousands of years ago. As pointed out in pg.15 “All problems are calculated like recipes and only with concrete numerical values. In these early times, men had neither a method to express formulae nor abstract quantities.” This makes me appreciate more about their ability to express and understand their thinking without algebra. Furthermore, this makes me think and excited about the possibility thousands of year later, would Mathematicians invent/discover a different way to apply what we call “calculus” (or any other topics) today. 

 

There are no questions that algebra has taken the field of mathematics a long way. Through this assignment, I began to realize how much I have programed to rely on algebra to understand Mathematics. As a down fall, it blinds me from understanding math in a visual and logical way. The way that Egyptians and Babylonians were forced to reason and think without the help of modern Mathematics. The way we fist attacked the problem was to do a lot of equation manipulations as mentioned above. It was until the later stage of our preparation we came across Gerde’s paper on “Three Alternate Methods of Obtaining the Ancient Egyptian Formula for the Area of a Circle” and realize the power and beauty of deductive and inductive reasoning in everyday life. The biggest lesson I got from this assignment is realizing that studying the history of Mathematics is not about looking back at how people used to do things, but providing myself another perspective to look at what I already know.

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