Assignment 1: Self Reflection

    Firstly, I would like to thank my groupmates Appu and Lisa for their hard work. It was a pleasure collaborating with them and putting the slides together. I had fun preparing the slides and presenting in front of everyone.

    I learned new terminology that I've never heard of before, namely, sagitta. It was particularly interesting to learn about sagitta because I remember in high school, we mostly focused on other terminologies such as chord and arc. I remember sagitta wasn't really applicable to the content I was learning. I've learned more about the sagitta when deriving the formula. The sagitta has two components - the minor segment and major segment. That is why the formula has the ± to distinguish between the two. The textbook only addresses the negative component (minor segment) and I had a difficult time deriving the formula via modern method because the formula in the textbook was wrong. 


 




    Another follow up I found interesting was the ancient method of solving for the chord, c. If C' is the circumference, they derived the formula, C'=3*d where d is the diameter. The Babylonians used the approximation for the symbol, π . Regarding that, when I found the modern way of deriving the formula for the chord, C', I've noticed a difference. The modern approach involves using the exact value of . However, to affirm the Babylonians used an approximation for π, substitute d=C'/3. It was interesting to learn about the approaches of ancient math and modern math.

    Lastly,  my groupmates and I had a long discussion on what our extension questions should be. We ended up with the following statement: 

Equal chords of the circle are not equidistant from the centre.

    I've learned that we could alter the statement by adding NOT to make this statement that was originally true, to become false. Aside from that, I've learned from asking the class to do the extension on the board, there were multiple different ways of solving for it. It reminded me that for math, there are many different ways of approaching a problem and deriving the answer. I often wonder how in ancient history, what mathematicians had to do begin solving a problem. 
    
    Overall, by working on the assignment and presenting it to the class, it was a great learning experience for myself and the rest of the class!

Reference

Scriba, C.J. & Schreiber, P. (2015). 5000 Years of Geometry: Mathematics in History and Culture (English Edition).                         Birkhauser.


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