Categotry Archives: Extended Essay (EE)

The title says it all.

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Extended Essay: Interim Reflection

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Categories: Extended Essay (EE), Reflections

So far, I’ve conducted about 4-5 meetings with my extended essay supervisor. Referring to my first EE reflection (first meeting), I carried on with my research about the different methods to solve various polynomials. Before researching in-depth to my main focus subject, which is cubic problems, I decided to include some formulas used to solve quadratics. The reason why I did this is to provide myself with more methods that I can look into, therefore I can relate the patterns and reasons why and how quadratics are related to cubics.

After listing important points down about quadratics, I started researching on cubics. I’ve found two mathematicians from Italy, which are Fior and Tataglia, who had a public mathematical competition between each other, regarding methods on solving cubic equation. I think these mathematicians are interesting and is worthy of mention in my extended essay, because they’ve invented a unique method to solve cubic equations without knowledge of imaginary numbers. Based on this discovery, it gave me the idea to explore complex numbers as well. I’ve also had a wonderful opportunity to meet Katie Steckles, who is a mathematician from UK, to come and visit our school. Her visit allows me to discuss about Fior and Tataglia’s method and recommend me helpful resources that I can go through to help my research.

Now, I’m starting on writing my extended essay and I am going to explore the application of these methods to a greater degree of polynomials. Explaining why and how methods work is a great challenge and definitely requires time for me to understand. In the near future, I need to dedicate more time in order to fully understand why and how these methods work in order to be able to explain it well in my extended essay.

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Extended Essay: First Meeting

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Categories: Extended Essay (EE), Reflections

Image source: https://www.youtube.com/watch?v=Zca-gVo-cPU

On my first extended essay meeting with my supervisor, Mr. Mahoney, I introduced him to the topics that was chosen from my proposal: Leibniz and Newton’s calculus methods. I was planning to analyse the two methods and determine which method is used more in the daily life. Mr. Mahoney made a great point that I have no criteria to “assess” these calculus methods (Used more in daily lives in terms of what? For a mathematician? a student? a teacher? and used for what?). Then I shifted and explained about my second topic which is solving cubic equations with origami. We came to a conclusion that this topic would work more as an extended essay, but before I get started, I need to do more research about this topic. This meeting ended with myself walking away, needing to do more research, and that I need to come back and tell my supervisor more about it.

However, before the second time I met him, I decided to change my topic into a comparative study of solving cubic equation (the combination of the early two topics that I have). So I explained to my supervisor that I will be researching different methods of solving cubic equation and do a comparative study of each of the methods in terms of efficiency and accuracy. Finally he gave me a thumbs up and said that I can start jotting down all the different methods that I could find. He’s also looking forward to see one of the most interesting methods that I found and he has never saw it before!

So, my task right now is to investigate different methods of solving cubic equation and document them together as well as all the resources I found.

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