Jackson's Math History Blog

Link to audio: https://drive.google.com/open?id=1tG8R-RWQ3-1J7cfVmI2qnMV24BSE3Gy0

This week's reading presents several interesting topics that I could potentially introduce to my future students, in particular the part about how numbers can be interpreted in terms of qualities and emotions. However, I think these ideas are to be presented as a side note to the main teaching topics because of time constraints within the classroom as well as information overflow. Since most students probably have heard about the association between numbers and fortune/misfortune from their parents, teachers can also try to tie in the personalities portrayed by the Mayan glyphs to "decorate" mathematics and draw students' attention. From my personal experience, I believe numbers can represent a diverse set of qualities in some situations. In sports the athletes are always assigned numbers on their uniforms, and depending on the sport, each number is often associated with certain qualities or positions. For example, a player with the number "9" in so...

From this week's reading, my main takeaways are the following: 1. The Romans rejected many of the mathematical ideas that interested the Greeks because what the Greeks focused on was too impractical. This can be explained by some of the cultural or social differences between the Romans and Greeks, where the author mentioned that Romans enter 'adulthood' sooner than Greeks, and thus the skills acquired during the early education years would not be the same across societies. Even today, what children are required to learn in one place may differ from those who grew up in another part of the world. 2. There is confusion regarding the terms "logic" and "logistics", particularly concerning their practicality and functionality. From my own understanding, I have always separated their meanings without considering if there is a possible connection. As stated in the article, logistics deals with numerable objects, and it was considered a study for slaves, ...

I was amazed by the creativity that the authors put into using modern dance choreography to represent mathematical proofs. Before this class, I had never thought about connecting math with arts in this fashion. As mentioned by the authors, "proofs unfold over time in a way similar to the sequential moves of a dance", and the math concepts can definitely be embodied through artistic representations. What I find interesting is how the dancers used intuition to make geometric shapes and imagining that the arms can represent equal lengths, because it's almost impossible to create precisely measured lines without any tools. At the same time, they can also be flexible and have unequal lengths to fit the parameters of a proof. I think using the body to guide the mind through geometric representations can be very helpful to the understanding of the mathematical ideas, as it provides more clarity with step-by-step movements rather than just static images on a piece of paper. ...

The long-lasting nature of Euclid's works, including The Elements , widely considered the definitive textbook for geometry, is most likely a result of the comprehensiveness of the ideas presented and the visual appeal it had to readers. It is also said that the book has influenced several prominent scientists throughout human history (such as Galileo, Kepler and Newton), paving the way to many of the scientific innovations we know today. Many have claimed that the logical representations in Euclid's book, as well as the consistent way in which he presented his ideas, are unmatched by any other. As a result, it is still the main textbook in the realm of geometry, and other books in the field all adopted Euclid's material. As mentioned, one of the main reasons that The Elements has been successful for centuries is the aesthetic nature in which Euclid explains the development of geometry. The propositions and theorems in the book can all serve as a front-row seat to view...

Our group presentation on the Pythagorean Triples went as planned: we presented the theoretical background and the ancient methods of solving right triangle problems, as well as discovered an interesting extension of the 3-4-5 triangle. The reason for choosing this topic was that we found the Pythagorean Triple concept to be both very intuitive and easy to understand. To me, this extension was probably the most interesting part of our presentation, as it stretched our conventional perception of the 3-4-5 relationship even further to higher powers. However, the challenge was to understand the reasoning behind the extension, which was an idea brought up by many other mathematics scholars, and why the cubic relationship does not hold for the other Pythagorean Triples. Moreover, the Mayan number system wasn't discussed in full during the class, so it was difficult to fully grasp the link between the 3-4-5 cubic relationship to the Mayan Long Count at first. After spending some time...