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. ...
The use of unit factions is convenient for everyday applications where we need to divide a set of things among an unequal number (usually larger) of individuals. For instance, suppose a group of eight friends wants to share three pies in equal portions, how can they accomplish that? A straightforward division would not solve this problem because 3 divides 8 equals 0.375, and the presence of decimals complicates things even more. I think by representing a fraction like 3/8 as a sum of two unit fractions (ie. 1/4 + 1/8) makes this kind of sharing problem much simpler. We can now infer that each person will get a quarter of a pie and one half of another quarter of a pie. Since dividing by half (or into quarters, one-eighths, etc.) is practically easy to do, this method could be useful for many similar problems, including the inheritance problem posed on the blog. If the man's inheritance is to be shared in 1/2, 1/3 and 1/12 parts among his children, then adding these unit fra...
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!
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