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Math, History, and Art

https://docs.google.com/presentation/d/1FL98Db7-5L8xFBSnnWn6tXbSuWfY06bNPEYtN-HBJmA/edit?usp=sharing My topic was on perspective and projective geometry. My presentation contained a brief history of perspective in art in the Renaissance and as I was doing my research, I found that I ended up talking about more math than I expected to. I found the math and theorems to be really interesting since up to that point, I had only viewed perspective from an artistic lens and looking into the math behind changed my perspective (haha). The art I did was of our math classroom and it was the first piece I did where I actually drew the perspective grid and followed it along. I chose to do a fish-eyed lens look and it was pretty challenging and I learned a lot. I tried to include a lot of what we learned in class in the drawing to look back on to. I forgot to take a picture of my art piece, but I donated it to the classroom. References: Andersen, K. (2009). The geometry of an art: The history of the...
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Embodied Mathematics

      The most interesting thing for me was at the beginning of the article, when Ascher was talking about types of maps. I never really thought much about the  Mercator projection version of our world map, but the article made me realize that the world wouldn't translate so easily onto a flat sheet of paper because the world itself is not flat. The distances of the world map we see most often are actually not accurate, and Mercator projection conserves alignment rather than distance. It was an interesting thought experiment to think about different types of maps and then for the text to relate what we just thought about onto Marshall Island stick charts.     In the context of Marshall Island stick charts, embodied mathematics is important as the charts themselves are mathematical models of the the physical world. It links real concrete information to something we can visualize and digest. Ascher also mentions that navigators must lie down and feel the way ...
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Assignment 3 Proposal

 Topic: Perspective Secondary school tie-in: Transformation geometry (translation, reflection, rotation) Method of presentation: drawing Tentative Sources: - Math through the ages (William P. Berlinghoff) - The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge (Kirsti Andersen) - An Introduction to eh Foundations and Fundamental Concepts of Mathematics (Howard Eves and Carroll V. Newsom) - The Invention of Infinity: Mathematics and Art in the Renaissance (J.V. Field) - Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century (Jeremy Gray)
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Arithmetic of the Medieval Universities

"The very word "liberal" implies that these arts be longed to the education free men not to the technological training of slaves." (pp. 264)     This quote really helped frame the purpose of Greek education. I never knew this before reading it now, but it makes a lot of sense. Many topics in the liberal arts are those that have little practical usage, and that you don't people who are struggling to make ends meet to study. I think it's interesting that the ancient Greeks explored so many proofs in mathematics as you don't need  to prove something works in math if you know how to use it. From the quote, I now know that the people studying these topics were probably very well off and could afford to spend time to think about subjects like this. I sound very critical, but I think these contributions that the Greeks made to mathematical concepts were really important. However, they also sound a little snobbish when they reject subjects such as medicine to be...
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Euclid

      Edna in her poem  Euclid Alone has Looked on Beauty Bare implies Euclid's work to be beautiful, "intricate", and "luminous." From my understanding of the poem, I would take Beauty in this context to mean the strange beauty of mathematics and of the natural world. Euclid was known for his study of geometry, and in his proofs, there is a Beauty that underlies the math. That Beauty was there before Euclid looked into them and it is there after, but Euclid was one of the first and so he saw the Beauty Bare. I know I would probably not be able to think of geometry like Euclid did. I can see the Beauty after my schooling and after things have been explained to me, but if I had next to nothing like Euclid did when he wrote his propositions, I don't think I could see all he did. Part of the reason Euclidean geometry has been so popular all these years is because of this simplistic beauty. Shapes are something we grow up seeing, and Euclidean geometry consists ...
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Dancing Euclidean Proofs

       The first thing that made me stop and think was this video concept in general. I think it was a really cool way to demonstrate proofs, one that I haven't thought about before. It's neat because when talking about geometry, I find myself gesturing and making shapes with my hands often, but never with my entire body. The other thing that made me stop and think was after my initial appreciation of the art form, I wondered if I had just seen the video without having worked through the proofs in class first, if I would have understood it just from the choreography. The first two dances, we worked on in class and through doing them, I understood what was happening and could follow along with the dance as I recalled my own thought process as I worked through. The third one was new to me, and on my first and second watch, it was hard to follow. For me, doing the proof first enriched the experience of the video and I could immerse myself with the choreography. I wonder...
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Was Pythagoreas Chinese

 I think it can be important to our students if we acknowledge non-European origins of mathematics. In the past years, we’ve been hearing so much that media representation of minority groups matter and there have been many stories of representation being meaningful for children growing up. The same concept should apply in schools, and students will feel much more seen and recognized if not all the mathematics is shown through an Eurocentric view. I know when I was younger, I was always excited to hear about Chinese contributions to modern math and science such as the invention of paper, gunpowder, and the compass. Learning non-European roots of math can create a more diverse learning environment where students feel more comfortable to learn and participate. It also opens up opportunities students to relate and share aspects about their culture. In regards to the names of concepts such as the Pythagorean Theorem and Pascal’s Triangle, I think it’s alright to teach them as is. The na...
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