Course Overview

I learned a lot in this course. I especially liked the classes when we learned about the ancient ways of doing math that are so alien to us. With writing systems so different, I would think that their thinking process would have had to of been different as well. I remember learning that the Mesopotamian's did not have the concept of angle, and had to think of different ways to solve problems. Who is to know if we are missing some glaringly obvious construct and are therefore limited in our understanding of our world?

I liked when Susan brought up the point that no one knows what do do when dividing by 0. It broke my brain, and now I wonder if this is the symptom of an imperfect math system. I also think of Goidel's incompleteness theorem, and about how there is a hole in maths. I wonder if this hole's existence is also a symptom of the same thing? Perhaps the students in 442 two hundred years from now will learn about us, and how we were so glaringly missing something that it seems incomprehensible to not understand.

Math Art Presentation Reflection

 This project was really cool in that it made me recognize a skill I have that should help me in my career as a math teacher. I was a self taught computer coder, and have decent knowledge to make computer programs. It was difficult for me to think of ways that I can incorporate coding into my teaching career, and I expected to not code much in my future. But now I realize how useful this medium could be for me to convey ideas to my students via art. I never though of computer coding as an art, but I realize that I can use my computer coding to create art!

My favourite piece to come out of my project, as I mentioned in my presentation, was Jupiter's perspective of the solar system, and this is the art piece that I've chosen to officially submit.

 

Orbit Executable

Please download this program and play around with it (doesn't work on Mac though) 

https://drive.google.com/file/d/1aeCC08e7us883Vd6z_PnMjnvSWpa9k3M/view?usp=drive_link

Art History of Math - Orbital Mechanics, Heliocentrism, and Vector Addition

 Our art project reflects the history of astronomy and actualizes historic beliefs using the mathematics of vector addition. There was a time in human history that people believed that all the heavenly bodies orbited around the Earth, an idea called geocentricism.

We have been taught that the earth and the heavenly bodies orbit the sun, but why do we think this? Occam's razor states that the simpler answer is the solution. If we were to monitor the paths heavenly bodies take as they pass through the sky, we would expect these paths to be simple.

Tracking the orbits of heavenly bodies from Earth, their paths are very wonky. It is only when we assume that the sun is the center of the orbit do the paths of the planets become nice ellipses.

By using the math of vector addition, we were able to simulate the paths heavenly bodies take while moving through the sky from the perspective of different planets. The assumption of Geocentricism creates beautifully complex patterns in the paths of the planets. We extended this to allow for the perspective of each planet being at the center of the solar system.

The paths of the planets are beautifully complex, and it is only when the Sun is the center of the solar system that the complexity dissolves to simplicity.

References:

https://journals.sagepub.com/doi/epdf/10.1177/002182860203300301

https://link.springer.com/referenceworkentry/10.1007/978-3-319-02848-4_926-1

https://link.springer.com/referenceworkentry/10.1007/978-3-319-02848-4_67-1

https://link.springer.com/chapter/10.1007/978-94-011-4179-6_10

https://link.springer.com/chapter/10.1007/978-94-011-4179-6_7

Medival Islam Mathematics

This article was really interesting! the first thing that stood out to me was the abundance of visual proofs. The fact that these proofs were originally done in a different language, yet I could easily understand them just from the visuals shows how math is this beautiful art that transcends language and cultural differences.

I particularly enjoyed looking at the mathematical 2D art. Seeing how such beautiful, intricate designs could be created from the simplest of rules blows my mind. Just by inscribing a square and rotating it over and over again to infinity, a beautiful pattern emerges that resembles traversing down an inter-dimensional cooridor.

Finally, I enjoyed learning about the Bagdad House of Wisdom both in class and in this article. Personally, I prioritize the synthesis of knowledge over the discovery of facts. I enjoy combining ideas into bigger and better things. The Greek, Hindu, Syriac-Persian, and Hebrew texts were the building blocks upon which synthesis was performed. 

Numbers with Personalities

 When I think of the Ramanujan story, I think that when he says each of the integers were his personal friends he meant that he knew an intimate facts about each number. He knew that 1729 was interesting because it was the smallest number that could be written as 2 different sums of cubes. He knows interesting facts about the numbers as a person in a small town knows interesting facts about all the people they walk past. I understand that Major's paper implies that he saw personalities with each number and befriended those personalities, but I personally do not believe that to be the case.

The only aspect of this article that I would implement in my classroom is the idea that the words we use to describe the numbers are not the same thing as the numbers themselves. It is important to connect the numbers to the words at a young age while the concept of quantities develops. However, once the idea has been cemented, it is important to break down that idea and understand the quantities in their true abstract form. By seeing quantities as abstract, we have accomplished the greatest mathematical breakthroughs. 0, negative numbers, imaginary numbers, etc.

Unfortunately I do not relate to this article in any way. I understand that I must be open to these ideas for I will have students enter my class who relate strongly to these ideas. In my class, I will act similar to an atheist who is accepting of those who have faith. While I do not agree, I would never dampen their belief system.

Trivium & Quadrivium

 Three things that stood out to me in this reading were:

1) The distinguishing between liberal education and technological training. I feel like in today's world, we are much more focused on the technological training so that students can "contribute to society." I do not describe myself as anti-capitalist, but I do recognize how much the arts is pushed aside in order to make profits. At the University of Alberta, the engineering building got a brand new floor with interesting patterns engraved in stone. This flooring cost more than the yearly budget of the entire performing arts department. I feel that this idea of knowledge as a liberal education has been lost in favor of progress. When student's ask "when will this be useful?" I realize that I don't need a practical answer, the concept of being intrigued by its beauty should be enough.

2) The importance of Easter in keeping math alive through the European middle ages. The amount of times this article referenced determining Easter was intriguing to me. Members of the clergy had to have math knowledge solely to solve this singular problem. I realize how different things are important at different times. In our time, it is the math of binary operations and logic that fuel our society, it would be interesting to read a similar article in the future that looks back upon our years and recognizes the fascination with a certain aspect of math.

3) The intertwining of numerology and mathematics. It is well known how much religion influenced the European middle ages, but I did not realize how much religion influenced the math at the time. This article paints even Pythagoras in a different light, for I now see how strange math becomes when it becomes deified. To think of numbers not as interesting in themselves but the key to unlocking their god. Maybe I shouldn't be so critical, because one could argue that the current scientific method is doing a similar thing. All humans want to access the secrets of the universe, some just think they will take a different form than others.