Jovan Choongh - Math History

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...