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...
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. ...
My first impression of using the number 60 as base rather than 10 was simple: I thought of the clock system we use today. There are 60 seconds within a minute, and 60 minutes within an hour, so it made sense. Perhaps 60 was the "original" base number, but the number 10 was used later in many other scenarios to make counting much easier (akin to how the Chinese language was simplified). The number 12, which is a factor of 60, also serves significance in the Chinese culture, where the 12 zodiacs play a major role in people's beliefs, values and even social behavior. It's also interesting that how the square of 60, which is 360, equates to a full circle in degrees. Since the Sun and Moon were divine symbols in most ancient cultures, the number 60 could hold also significance. This was prior to being introduced the historical background of the Babylonians and doing the in-class activity with my peers. Further research into its origins somewhat confirms that I was on th...
Hi Jackson. Your song is beautiful, and your presentation was very good. Do you have your slides that you could post here as well? Thanks!
ReplyDelete