Jovan Choongh - Math History

Reflecting back on this course, it has been one of my favourite courses taken in my entire university career. I feel as though the interactive lectures and engaging history lessons were very fun.  I really enjoyed learning different methods of solving mathematical problems and different ways of conceptualizing mathematics. Specifically, when looking at how the Egyptians went about completing multiplication and division, I was in shock because growing up we were only taught a select few methods, and any new method or perspective is very counter-intuitive, thus, learning the Egyptian method was critical in widening my scope on how important the history of mathematics is. Egyptian mathematics continued to resonate with me, I also really enjoyed learning about regula falsi and the method of false position, and how its expansions give real intuition into modern day algebra. For me, to think of a world without the existence of algebra is absurd and thus reading about Ahmes and regula...

Manvir and I did a short story geared towards secondary math students where the story incorporates modern day football and a historical lesson on parabolic motion. Thinking about the history of math, I think one of the centric themes of this course was to be able to tie in history of math into practical lessons to teach your secondary students. Thus, we looked at the maths that go into throwing a football, and how fundamental parabolic trajectory and projectile motion are to the sport. Therefore, our idea was to use a possible scenario where the quarterback wants to throw further independent of strength, and what parameters of his throw he can change (as per parabolic motion) to increase distance in the horizontal direction. We did a deep dive into how Galileo proved the fact horizontal and vertical velocities are independent components, and what parameters affect each vector. After our research, we decided a short story/play would be a very interesting medium! -- The...

Project: The history of throwing javelin and the mathematics of objects with parabolic projections. Javelin was first seen in the Ancient Olympic Games beginning in 700 B.C. Manvir and I plan to dissect the origins of mathematical analysis where ancient mathematicians attempted to improve  throws using calculations. We will then integrate a tie-in to modern throwing of objects and discuss modern maths around parabolic projections and how the weight of objects comes in to play. We will be performing a demo video.

I would definitely introduce these ideas as a teacher to secondary math students because of the imagination involved in attaching personalities to numbers could be inspiring to certain students. Additionally, it was interesting to read Major's perspective on social numbers and the experiences of individuals who have OLP; imagine teaching students who have never heard about synaesthesia and how individuals can make deep connections and pairing with abstractions such as letters and numbers. Perhaps, this would enable secondary math students to think of math in a perspective never taught to them before. Additionally, I think Major's discussion on personal cultural associations with a number is a sleek way to tie in history, adding a personal touch to a variety of cultural backgrounds to connect with a diverse group of students. I was shocked to learn that "in the Korean and Chinese languages, the unlucky quality of “four” is connected to the fact that it sounds like the wor...

Prior to this reading, I knew nothing about the development of medieval arithmetic and its progression from the trivium and quadrivium. Thus, it was shocking to learn that the processes of defining liberal arts and what studies should be rudimentary to one's education were discussed in medieval times over 2000 years ago; an important topic of discussion regardless of era. I was overwhelmed by the sheer fact many of these ancient Greek and Roman philosophers such as Plato and Seneca were concerned in the composition of education and what should be taught and for how long. Additionally, something that really made me stop was ancient Greece's definition of "logistics" where they wanted differentiate the arithmetic of business from the study of number, which was solely "arithmetic." Subsequently, the greeks differentiated logic from logistic, where logistic was a study for children and slaves, whereas logic was for the "free man." As I read I cont...

Reading the discussion in the paper about the designing of the dances fascinated me because of the intuition of the authors to relate the steps of the geometric constructions of the propositions to the the sequential nature of choreography; quite logical inspiration produce such a short film. Additionally, the notion that "proofs unfold in time" similar to dance is intriguing, and makes me think of mathematics in a completely different way. Never had I pondered mathematics being used to choreograph a dance before, and now I think that perhaps dance is essentially mathematical in its nature. I really enjoyed watching the simplicity behind Proposition 1 because I believe it can be embodied quite well by the human limbs in a way that is intuitive to visually perceive. At the end of Proposition 1 dance, the ease of which the arms match (the close approximation) is amazing in its analogy to an equilateral triangle. When Manvir and I attempted to execute dancing Euclidean proof...

Euclid I think Euclid and Euclidean geometry has remained relevant and continually studied throughout history because of the consequential construction of concepts Euclid builds throughout Elements. The first six books, which dealing with plane geometry, attempt to build and demonstrate very basic properties of shapes and geometric elements such as triangles, parallelograms, squares, and rectangles. I believe that Euclid's laying of such fundamental ideas on basic plane geometry is what lures individuals and scholars to constantly refer back to his work. Additionally, as scholars recognized his work as remarkable and respected the vigour, it became the "primary source of geometric reasoning" as stated by van der Waerden; when the mathematics community recognized the clarity of the Elements it created a snowball effect of its popularity. Referring to Proposition 6 from Heath's translation of Book 1 of the Elements, I believe this is a principle we are ta...

Assignment We were solving Problem 10, which was Ahmes' loaves problem of dividing 100 loaves amongst 5 men with two constraints. 1) The share distribution must have an arithmetical progression ie. 1,3,5,7 2) 1/7 of the three largest shares must equal the two smallest shares. Here is a link to our presentation: https://docs.google.com/presentation/d/1vRxEetktPO_QzsxoKWlQ3kTzT5uRsVXtRfJuyeLvTCM/edit?usp=sharing Reflection Beginning the assignment I was quite unfamiliar the regula falsi or the false position method, and had only heard about it when Susan first touched upon it in class and using it in simple algebraic multiplication. Working with the false position method to solve this problem was fascinating because I could see the intuition and the building blocks forming for modern algebra. More specifically, for this problem in modern mathematics one could use simple algebra and a system of equations (or substitution), however, the fals...

To answer the question of whether teaching students about non-European mathematics makes a difference on their learning, one must reflect upon the definition of "understanding." Referring back to our class discussion last week, strong mathematical "understanding" is confidently being aware and familiar with not just one, but several approaches to a topic of mathematics. The different approaches whether they are Pythagoras or "gou-gu" have interrelations which open the brain to thinking about a topic in different ways. Additionally, the different approaches may have been used for different applications which enables students to come up and learn more use cases about the topic, I did not know that the "gou-gu" mentioned by Chen Zi was used to calculate the distance between the sun and the earth using a shadow cast by the sun. Personally, learning different historical approaches broadens my own horizon pushing me to a better understanding. It...

It really puzzles me that on the surface there seems to be a sense of practicality in the Babylonian word problems which is a complementing contrast to the theoretical, abstract Greek mathematics, however, when diving deeper practicality diminishes. Robson addresses a valid idea in that Babylonians may have surpassed the needed amount of word problems for actual applications, and that problems which addresses real life applications which were getting outdated. Hoyrup's perspective on the notion of Babylonians utilizing applied mathematics and word problems to illustrate abstract contracts is enticing, giving intuition into absurd numbers and unknowns which were in some of the Babylonian word problems. Perhaps, exists some form of mathematics where once practical applications have been exhausted, mathematicians and practitioners now seek to exercise mathematics for the sake of exercising mathematics and "solving" some sort of problems. The latter which then results i...

Originally 12 = 1/12 + 1/3   + 1/2 12 = 1/12 + 4/12 + 6/12 With one less horse 11 = 1/2 + 1/3 + 1/12 11 = 6 + 4 + 1 Assuming round 1/2 of 11 is six horses, and 1/3 of is four horses and 1/12 of 11 is one horse. The allocation using unit fractions does not change. The benefits of unit fractions from Ancient Egyptian times still exist today, when dividing or allocations n number of items amongst x people, giving the unit fraction x/n, useful back then in rationing and still today.

I find it very fascinating in which the ways Babylonians denoted mathematics in certain notations when no such thing as current algebraic notation existed.  The fact Babylonians utilized words such as "ush", "sag," "lagab," and "zud" to symbolize different unknown quantities Prior to algebraic notation, stating mathematical principles was done through the usage of statements, tables, and numerical tablets dedicated for specific principles. I believe that mathematics is about reproducible logical statements, I think you must generalize in the sense of being able to substitute specific numbers for a general span of numbers n, and the statements must follow certain steps. I do not think one must be abstract entirely when discussing mathematics, I think that specific examples provide intuition. However, generalization and abstraction lead to logic which is reproducible without using specific numbers. In the case of the Babylonians, their refere...

Column I           Column II 2                       22,30 4                       11,15 5                       9 6                       7,30 12                     3,45 20                     2,15 30                     1,30

The first thing that surprised me was the ignorance of research pointing to the development mathematics in Mesopotamia and Egypt, and the sole focus of the classic Eurocentric view that mathematics is a "product of European civilization." I had never heard of such a view establishing Europeans as the sole developers of mathematics as stated in Figure 1.1. Another astonishing notion was the fact India was a key centric geographic location for the transmission of the mathematic ideas, and that the Indian had established itself significantly before the Ptolemaic Egypt and Rome's Eastern empire had established itself. I had no idea India had such an influence on European sciences and medical studies, where Greeks highly regarded India's studies on medicine. I think it was also fascinating to learn of the medium of transmission which the Arabs played in transporting key mathematical concepts originating from India and China. In all honesty, I had never delved much into...

60 may be convenient and/ or useful as the base for a number notational system because of size, where perhaps the Babylonians lived in tribes or clans of 60 individuals rather than 10 which is quite small. Another speculative guess may be that 60 is the number of Gods or deities Babylonians worshiped, or that the number 60 has cultural significance in terms of religious events or phenomena. 60 may also be approximately the number in which a certain significant crop grew or yielded or sold that was consumed on a regular basis. 60 is different from 10 because of the number of factors it has relative to 10, whereas 10 only has four factors. 60 is of course, still used in our current time-telling system in which it the basis for minutes and seconds where 1 hour and 1 minute are composed of 60 minutes and 60 seconds respectively. 60 is also significant because of the number of days of year is approximately 360 which is divisible by 60. I would also speculate that Babylonians were able to a...

Prior to reading the article regarding the integration of mathematics, my preconceived notion of incorporating history into math was simply that math history should be taught to an extent, such that reasoning for the existence of the subject is logical. Moreover, I believe that history of math is crucial for secondary students and university in understanding the fundamental building blocks of concepts for mastery. The history of mathematics and its applications in history enable students to appreciate a sense of feasibility of the relevant concepts being taught. I still remember going to watch a math play at a performing arts center in Surrey as a part of my ninth grade high school math class, and being in awe of Eratosthenes' calculations of Earth's circumference.  Getting out on a field-trip really made me appreciate math in a way where I began to see how profound applications could be. Reading upon the segment of using historical problems as platform to integrate history i...