David's Mathematical Blog

The most interesting part of the article for me was the fact that Marshall Island’s navigators' knowledge and techniques were highly prized and well kept secrets. The fact that the knowledge was a well kept secret within relatives of the chief is interesting because I think that the people value their knowledge much higher than other things, that knowledge gives them power. One thing that concerns me is the event that a navigator becomes unable to navigate the boat due to illness or death. In that case, I am curious if there are other people on the boat who are able to interpret the maps and steer the boat in the right direction. I think that embodied mathematics in this article is apparent in the fact that navigators use their experiences on open water to construct an accurate map of the surrounding atolls. They were able to identify patterns in the waves and swells to locate positions of land relative to each other. Embodied mathematics is significant in history because math is u...

The topic I will be working on is constructing conic sections using historical mechanisms.  Draft references: Shell-Gellasch, A. (2007). Hands on history: A resource for teaching mathematics . MAA. I will attempt to create van Schooten linkage(s) that can draw ellipses, parabolas, hyperbolas.

“Considering specifically the field of mathematics, 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” (266). I find this quote to be surprising because I had expected neither of these to be that important compared to the expected theological knowledge. I also find this interesting because information is readily available if we look for it, but the people from back then had to use a method to determine the date of Easter. “He ends with a naively pious interpretation of the first seven digits: one God, two Testaments, three Persons in the Trinity, four Gospels, five books of Moses, six days of Creation, seven Gifts of the Holy Spirit” (268). I reflect back on a previous blog post where I was asked to explain any significant number that I had, and I had said none besides information about myself such as my birthday. From this quote, I wonder if these numbers were actually planned or i...

The poet describes how Euclid describes his own works as “Beauty bare”, which I interpret as beautiful because it is simply the truth. Edna St. Vincent Millay writes that Euclid alone has looked on Beauty bare, meaning that only Euclid sees the beauty, whereas the people who prate stare at nothing. The author defines beauty not as “shapes of shifting lineage”, but as the truth. I think Euclidean geometry has been popular for many centuries because it is clear and simple to understand. If this were not the case, it would become harder to follow along and some people may lose interest. I thoroughly enjoyed learning about Euclidean geometry in high school because it is a very visual concept, rather than abstract algebraic expressions.

The first thing that made me stop and think were their decisions to differentiate the proof from the dance. The first decision was to trace out the entire diameter instead of just the radius by using both arms. Another decision was to repeat the dance multiple times to formalize the proof for the audience. I think that these additions would be extremely helpful to the reader if they were learning the proof for the first time. The second thing that made me think was the idea of incorporating oneself into the proof. The article mentions “humanizing” the proof and collaborating among one another. I find that proofs are often difficult to understand and follow through when they are written down. By having multiple people engaged and visually showing the proof, it is made more accessible to the audience. The activity in class was challenging, but fun. I think that although the activity was short, the students would be highly engaged when watching an arts based performance. One of the bigges...

After reading the article, I can say that teachers should be acknowledging non-European sources of mathematics. I say this because of two points: Europe is not the only continent in the world, and there are often many ways to solve a problem, as demonstrated by the Pythagorean Theorem and the Gougu theorem. The motivations for solving mathematical problems were different in each area. For the Greeks, they used math to pursue philosophical truths of the world, and in doing so, put a much greater emphasis on proofs. The Chinese used math more in the application sense such as land surveying, but also acknowledged the existence of purely mathematical problems. As teachers, we should help the students understand why studying math is important to them, since all students are different in their own educational pursuits. My thoughts on naming mathematical concepts is that the concepts should be named after someone who contributed most to its discovery. I also think that we should not dwell on ...