Group project -Applying the binomial formula

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Our group Project is 1.2.4:

In the text from the Seleucids’ era (BM 34568), obviously composed for teaching purposes, occurs a rectangle with the sides a = 4, b = 3, for whose diagonals d we are given the terms d = a/2 + b and d = b/3 + a. Then we are supposed to calculate the three pieces a, b and d by means of the quantities a + d and b or b + d and a. Other than that, we can use a − b = 1 and

A = a · b = 12, or a + b = 7 and A = a · b = 12.

a) Solve these problems according to the modern method!

b) Retrace the Babylonian steps of calculation by using the term (a + b)² −4A = (a − b)² passed down to us on clay tablets, in order to, first of all, calculate the difference a − b from the sum a + b and thereafter the sum and difference of quantities a and b themselves!


This is our PPT:
https://docs.google.com/presentation/d/1FsASoA7QqRUaOuKEkFRpz4ao2k-pwjKoL-1nAPdiKfA/edit?usp=drive_link

My reflection:

When I first saw the problem, I immediately noticed it was designed for teaching purposes, which shows that the Babylonians valued math education from an early time and used real-world problems to develop students' mathematical thinking. Who would've thought that ancient students had similar struggles to today's students? (Just kidding!)

To be honest, when we first got the problem, we spent quite a while trying to figure out what the conditions were and what exactly the question was asking. Clearly, this ancient math problem isn’t formatted like the ones we see today.

As I was reading the problem, I started wondering how they came up with the formula for the diagonal. Later, we found some steps of the proof, and I was even more impressed. But I’m still really curious—did they derive it through calculations, or did they measure it somehow? Anyway, we used modern algebra to verify their diagonal formula, and if they really figured it out through reasoning, that’s just amazing!

We also tried solving it using a geometric approach, and wow, the geometric method was so clear and straightforward! Looking back, I’ve always known what the Pythagorean theorem is and how to apply it, but I never really understood where it came from. I’ve been relying on formulas without ever realizing how beautiful the theorem is visually. Suddenly, I grasped the beauty of geometry—everything fits so perfectly, so harmoniously, with a certain elegant simplicity.



After solving this problem, I feel that despite the differences in time and culture, math really is a universal language that connects us all.

Comments

  1. Susan GerofskyNovember 3, 2024 at 10:21 PM

    So interesting and well written, Nanxi! An excellent project!

    ReplyDelete

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