EDCP 442 Reflection

This course has been one of the most wonderful parts of this semester!

Analyzing the relevance of mathematics to non-Euro/Western cultures and civilizations really highlighted the impact of the industrialization of education today. I love the journey we went through every class, that began with familiarizing ourselves with the contemporary applications, proceeded to historical roots, and then amalgamated old traditions in a present setting. It was so helpful for developing our interest and appreciation of those topics. The readings were very intriguing and paved the way for a lot of fun. The best part about this mathematics history course is that it deepened our curiosity for math in such a simple and transformative way!

Assignment 3 Reflection

Before this assignment, I had a 1-dimensional, surface level understanding of Newton's work with gravity and calculus. The research that went into learning about Isaac Newton's life was different from the research that we've been conducting in this course so far, and the reason there's that shift is because it wasn't just learning + presenting a few cool, chronological facts about Newton and his work- rather, it was important to understand his whole life, interactions with other mathematicians, influences, and strengths and weaknesses, in order to understand him and meaningfully present the whole Isaac Newton. The journey and process was so enjoyable and intriguing, and now I have a different sense of respect and appreciation for both Newton and Halley. Sometimes it's not just about what someone does, but the way they execute it, and that realization carefully emerged throughout the course of this project, and enhanced the overall takeaways. 

Assignment 3 Slides

The slides for our presentation can be accessed here:

https://docs.google.com/presentation/d/1Avh0az7NcbxiWt8zfcpltptt2Hw127ycxt_aiL9Ixlo/edit?usp=sharing

Medieval Islamic Mathematics

There was a great deal to take away from this one chapter in Berggren's 'Episodes in the Mathematics of Medieval Islam.'

For one, the depth of the biographies for Al Khwarizmi, Al-Biruni, Al-Khayyam, and Al-Kashi were very interesting. Each of them have very colourful lives and it’s quite fascinating to try and interpret how these experiences led to their mathematical discoveries- especially since they don’t seem to have that *reserved and otherworldliness* characteristic that is common among other mathematical biographies from the Renaissance era; their dedication, personalities, and interdisciplinary approach really stands out throughout the reading. For instance, Al-Khwarizmi made contributions to geography, cartography, and law; Al-Biruni debated the nature of light with Avicenna, and made significant contributions to comparative religion (I never would have guessed that he is quite notable for his work on India); Al-Khayyam was a poet; and Al-Kashi started off as a wandering scholar. I would introduce this to my students, because I think it will help deconstruct that stereotypical persona that so many of us have when it comes to mathematicians. 

Assignment 3 Plan

Kelsea, Marius, and I will be working on the life of Isaac Newton. I will capture a few elements of Newton's life on an embroidered piece (most likely an 8 inch embroidery hoop). The main image will focus on Halley's influence on Newton, but I will include small bits of Newton's work with gravity, optics, calculus, alchemy, etc. in subtle ways to add to the piece. 

Trivium and Quadrivium

"The Arithmetic of the Medieval Universities" by Dorothy Schrader was enlightening. Here are 3 points that stood out to me:

“Arithmetic was a study of the universities; logistic was not.” (266) The difference between arithmetic, as number philosophy, and logistics, as sensible numeration, was surprising. I wasn’t expecting that contrast between the two topics, especially in consideration of their present day unity. In terms of the evolution of mathematics, this is quite interesting because while the operations, theorems, and proofs withstand the test of time, certain vocabulary/notation, branch classification, and societal significance have changed quite a bit. 

"Numbers with Personality" Reflection

 Alice Major’s article, “Numbers with Personality” was delightfully intriguing! It connected so nicely to Myron Medina’s presentation on Mayan Mathematics, and I quite enjoyed learning about the head variants, social numbers, ordinal linguistic personification, mathematical elements of synesthesia, and Ramanujan’s taxicab number. Something that I found particularly interesting was that the Mayan’s visual connection with numbers overlaps quite a bit with Ramanujan’s personified relationship with numbers; perhaps it alludes to a connection between these types of learners and grasp of mathematics (and perhaps it doesn’t). Ramanujan’s remarkably exceptional ability to see numbers in the way that most of us couldn’t, no doubt led to parts of his success. And, what is certain, is that the relationship that we form with numbers, in terms of self and culture, has an impact on our perception of the world. 

"Dancing Euclidean Proofs" Reflection

Before reading the paper, I struggled to make a logical connection between geometric proofs and dance, and was fairly curious as to why they chose to represent Euclid’s proofs in that medium. As breath-taking as their choreography was, it simply wasn’t the rigorous and permanent style of proof that we’re used to. So, the first comment the stood to me was “our first step was to make explicit for ourselves that rationale for translating these proofs as dance.” And they provided marvellously comprehensive and convincing points as to why it made sense! Though the topic was specific, their arguments are easily applicable to expressing math in any form, available to all types of learners. Their embodied visualization is particularly applicable to visual, kinaesthetic, logical, and naturalist learners, which reiterates that learning math isn’t confined to any learning style, and directly synthesizes a hands-on experience with learning math. 

"Euclid Alone Has Looked on Beauty Bare" and "The Euclidean Domain" Reflections

Euclid of Alexandria, aka the 'Father of Geometry', has been given the honour of being one of the greatest mathematical thinkers of all time, due to his contributions to geometry and number theory. Not only are all 13 volumes of Euclid’s Elements an astounding and comprehensive explanation of mathematical ideas at that time, they also provided some source of inspiration to other greats such as Sir Isaac Newton, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, Bertrand Russel, and Ada Lovelace! Despite the fact that there is quite little known about Euclid himself, his works have paved the way for so many different topics in mathematics. Some of his most popular work include the 5 axioms of geometry, a prime number theory, a perfect number theory, and defining the greatest common divisor. 

Eye of Horus, Unit fractions in Ancient Egypt, and Special Numbers!

Research on the significance of the Eye of Horus:

The Eye of Horus is a very packed symbol! Not only did each of the fractions 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64 have denominators comprised of the first 6 powers of 2, they also represented Heqat fractions, which was an Egyptian measuring unit for grains and flour, and each of the fractions accounted for a different human sense. 1/2 accounted for the sense of smell, 1/4 for sight, 1/8 for thought, 1/16 for hearing, 1/32 for taste, and 1/64 for touch. I'm a bit curious as to why the fractions were allocated towards each sense as such; I would have expected that 'thought' would be paired with the largest fraction, 1/2, since it's deemed as the most important sense. One of the articles I read presented an insightful explanation as to why which fractions were paired with what sense, however, they concluded that their explanation was mere speculation that took Egyptian mastery of medicine, arts, and mysticism into consideration. After studying the Babylonian base 60 system, I find it really interesting that the Egyptians had a particular affinity to base 2. I'm surprised that the Heqat fractions didn't include 1/3 or 1/5, which I think would have been more practical as a measuring unit for grains and flour, than 1/32 or 1/64. However, I imagine that based on real-life situations of providing grains and flour for Egyptian communities, it might have been more convenient to have a base 2 system for rationing portions.