Jovan Choongh - Math History

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of word problems for actual applications, and that problems which addresses real life applications which were getting outdated.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...