Jackson's Math History Blog

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...

In my opinion, I believe attributing certain mathematical concepts to both Western and non-Western origins widens a student's perspective on the entire subject area and helps to take down any kind of "racial hierarchy" that the student may develop when learning math. It can change the views of students - especially those who came from a Western cultural background - on other cultures and their contributions to humanity. An important aspect mentioned in this week's reading is geographical isolation, which was likely one of the causes that ideas originated in China were overlooked. In today's digital world, it's important to emphasize the constraints in knowledge sharing that ancient people faced because had communications been easier, discoveries made within many cultures would have been accredited. On the other hand, what names are given to the mathematical theorems are not important. To me, introducing how other countries (eg. China, India) were just as p...