Math History Reflection （Duncan）

  Topic: Fibonacci Sequence and the Indigenous Dreamcatcher     I am going to create an indigenous dreamcatcher, which embeds the pattern of Fibonacci sequence. When we divide every Fibonacci number by a constant “k”, the remainder repeats after “n” numbers. I will turn this periodic characteristic into a visual representation and show it on an indigenous dreamcatcher.   Example of an indigenous dreamcatcher:       Sources:    1.       Weisstein, E. W. (2003). Pisano Period.  https://mathworld. wolfram. com/ .   2.       https://www.theindigenousfoundation.org/articles/dreamcatchers   3.       The So-called Fibonacci and Medieval Numbers India in Ancient Singh, P. (1985). The so-called Fibonacci numbers in ancient and medieval India.  Historia Mathematica ,  12 (3), 229-244.   4.       Fibonacci Sequence : History ...

  “course material fir a master’s degree is today common knowledge for third grade school children, and although some of the more profound medieval processes of ratio and proportions are today taught in eighth-grade arithmetic classes, medieval arithmetic must not be regarded as superficial or merely elementary”   “ In fact, ‘computus,’ which originally meant merely computation, soon came to be associated exclusively with the technical study of Easter reckoning.”   “ it is known that Church councils from the time of Charlemagne demanded that the clergy have a knowledge of music and be able to compute the date of Easter.”   The above three quotes are not necessary three thinking points I had when reading the paper. Instead these three quotes allow me to build on my feeling/response to this paper. Firstly, it reminds me of a previous blog post we did about “apply” mathematics and “pure” mathematics. As discussed earlier, as the belief and culture changes the idea of “p...

    Edna St.Vincent Millay believes Euclid has studied the fundamental elements of beauty. My guess of what it means is that all picture, painting or architecture that are deemed beautiful are made out shapes. As Euclid has studied lines and circles without colours or decorations, Edna considers they are the foundation element of beaty. Moreover, Edna believes not everyone can handle this bare form of beauty. This poem left me lots of questions. Edna is a poet, why would she consider the bare forms of beauty are shapes instead of words? I looked into her connections with artist or mathematician and couldn’t find any. The closest I have got is that she has a friend named Thelma Wood, who is a sculptor. The way she uses literature to express the beauty of Mathematics invites us to think about how do the opposite.   Instead of looking at Euclid’s work as the bare form of beauty, I believe many of us who studied Mathematics see it as the foundation of what we know now. His wo...

     This article makes me relate to two big ideas other courses have talked about. The first being allowing students to take ownership to their work. As teachers we always want to find ways to motivate our students. One of the best ways to do so is to allow students to establish a sense of belonging. On one hand, it is about having students feel they belong to the classroom. On the other, it is having students feel their work belong to them. Have students first plan out each move and execute with their own body definitely established a sense of belonging. Relating to me own experience, when I took the Euclidian Geometry course in my undergrad, I had to understand dozens of proofs. However, none of it was memorable for me.  Another idea that stood out from the paper and the courses I have been taking is about the indigenous way of learning. Through dancing on the beach, it sparks the "dynamic relationship between us and nature". As we continue to learn about the indi...

  If we were to acknowledge the non-European source in our classroom, one difference we will make as teachers is widen the horizon of our students. Since thousands of years ago the knowledge of math rely on the contribution of different people around the world, even long before University was a thing.     Throughout the years different culture and civilisation has shaped the Mathematics we teach. A singular Eurocentric view on Mathematics in classrooms undermines the contribution that came before us. Acknowledging non-European sources not only “give     credit” or “recognise” the contribution made by other’s but also introduce a different perspective on the same Math we teach nowadays.     The naming of this theorem could mis-led people to believe the Mathematical concept was discovered or invented by the person named after. In many cases, it may not be true. Take Pythagoras as an example. Egyptian was known to use 3, 4, 5 triangles in their ...

  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...