Assignment 3: Exploring a math history topic through making/the arts

Assignment 3 Tower of Hanoi

Nov 27 Medieval Islam Mathematics Reflection

The House of Wisdom is the first point that made me stop. While I was doing my presentation on historical integration, I came across Alhazen (Ibn al-Haytham) who lived over a thousand years ago. He had major contributions to optics and integration and was involved with the House of Wisdom. Initially I thought it was a group of collective individuals coming together to work on..discovering new things, though in fact it was primarily a library and a place for translation and research. The people in there would study ancient Greek mathematics/astronomy and further built on these topics. The one who established the House of Wisdom was Caliph alRashid. His son, Caliph al-Ma’mun, was the ruler who made the House of Wisdom so important. This caught my eye since the word "caliphate" means "an Islamic state, especially one ruled by a single religious and political leader". This word might've came from the two prominent aforementioned father/son. It also referred to the Islamic world during the medieval period, when Europe was in its dark ages while science and technology grew in the middle east. Furthermore it was interesting to how algebra and geometry flourished during the Islamic world which resulted in beautiful artwork captivating the eyes. A lot of the constructions with shapes inscribed within each other were mystifying too. Some circle geometry were shown as well with procedures I have never encountered in an elementary Euclidean geometry class. The good news is that many of these constructions can be replicated by hand with easy to follow instructions. This makes it friendly for school students to use so that they can create fascinating math works.

Nov 20 Maya Numerals

For the number "1729", Ramanujan noted that it was interesting because it was the smallest number expressible as the sum of two cubes in two different ways: Major's paper might discuss the role of intuition in mathematical discovery or the personal relationship that mathematicians have with their subject. Ramanujan's work often relied on deep intuition, which could serve as a prime example of this relationship. The collaboration between Hardy and Ramanujan, who came from very different educational backgrounds, could also be used to highlight how diverse perspectives can lead to significant mathematical advancements. If I would introduce this to secondary math class, mentioning these stories can be a captivating introduction to several math topics and would likely engage the students. The stories connects math to real world contexts, making it accessible and interesting. It shows that mathematics isn't just about solving abstract problems but can be playful and intriguing. For advanced students, exploring the proofs behind these math properties can deepen their understanding of mathematical rigor and methodology. In terms of numbers/letters having personalities, some might see the number 2 as a generator because it is even and small. It is also the smallest prime number. So many concepts seem to trace back to this number. The number 7 as more mysterious due to its associations in literature and folklore. The number 3 appears a lot as well and it's important since 3 is the smallest number of edges to form a closed polygon as well as having a triad stand to support a seat. In many languages the number 4 is dispised since it sounds like death. Dates such as Friday the 13th have had superstitious stories revolving around it which makes some people uneasy to write an exam at that time! 

Nov 8 Trivium and Quadrivium Article Response

The article introduced some interesting things. To begin, this article has a Latin title and it is separated into two parts, one of which has 3 topics and the other has 4. I initially saw this as a distinction between what is now known in modern day as the Humanities and STEM. This practice has been around since the medieval times. Either way, both of these parts required people to be literate and well versed cultured citizens. About 15%-30% of the population were like this back then. So there weren't that many opportunities for serfs and labor people to grow in their knowledge in these areas. However, looking at it today, most people can read and write, so the literacy rate has gone up. Many people are engaging in areas of both fields. Kids are learning a variety of everything in their young elementary years, and begin to specialize more and more as they get older. Another point that stood out was the different methods of division. There was the abacist method which was complex and cumbersome so it wasn't that favored, thus it got the name "iron division". It required a good understanding of the abacus and the ability to manipulate the beads to represent the division process physically. I personally had a hard time learning the abacus (mine was the Chinese suanpan) since there were some things to keep at the back of your head when doing the computations. On the other hand, the algorist method was simpler and more straightforward, thus it got the name "golden division". It used written calculations and was based on the Hindu-Arabic numeral system, which included the use of zero and place value, so it was more efficient to do the steps physically on paper. To get to this point wasn't that easy initially, as switching from the previously used Roman numerals to Hindu-Arabic numeral system took over two centuries. This newer method also allowed calculating the date for Easter much easier than before. I never knew why the date for Easter always changed annually, but it definitely is dependent on something, just like how the Spring Festival is dependent on the lunar cycles. Seeing now that Easter's date is determined by the Golden Number and the Dominical Letter and all the math involved behind it made me realize the complexity of the arithmetic people centuries ago had to perform. This, blended in with the fact that the clerics should know how to do the calculations emphasized the importance and significance this key date played in their faith.