Shawn-EDCP-442

Topic: Tower of Hanoi Puzzle Reference list: Shell-Gellasch, A. (Ed.). (2007). The Tower of Hanoi. In Hands on History: A Resource for Teaching Mathematics (pp. 29–33). Mathematical Association of America. Hinz, A. M., Klavžar, S., & Petr, C. (2018). The Legend of the Tower of Brahma/History of the Tower of Hanoi. In The Tower of Hanoi: Myths and Maths (Second, pp. 1–16). Birkhäuser Verlag.  MacDonald, Ayliean. Numberphile. (2021). Key to the Tower of Hanoi. YouTube. Retrieved from https://www.youtube.com/watch?v=PGuRmqpr6Oo. PurdueX CS180.1x. (2016). Intro to Towers of Hanoi . YouTube . Retrieved from https://www.youtube.com/watch?v=rYGEDlIB-4w.  Tower of Hanoi. from Wolfram MathWorld. (n.d.). https://mathworld.wolfram.com/TowerofHanoi.html Britannica, T. Editors of Encyclopaedia (2023). Tower of Hanoi. Encyclopedia Britannica. https://www.britannica.com/topic/Tower-of-Hanoi   Artistic format: Tower of Hanoi

Reflecting on the reading, it’s fascinating to see the significant role that the House of Wisdom in Baghdad played during the Islamic Golden Age. It was more than just a library; it was a vibrant center of translation and research where scholars translated Greek and Hindu treatises into Arabic and conducted their own research. This institution was instrumental in preserving and expanding knowledge during this period. The contributions of Muhammad ibn Mūsā al-Khwārizmī, a renowned Muslim mathematician, are particularly noteworthy. Al-Khwārizmī popularized the use of Hindu-Arabic numbers and the number zero, introduced the concept of algebra, and demonstrated the use of geometry to prove algebraic results. His treatise on Hindu-Arabic numerals played a pivotal role in popularizing these numbers and the concept of zero, which revolutionized mathematical computations. Lastly, the practical application of algebra, as demonstrated in Al-Khwārizmī’s treatise, Kitab al jabr wa’l-muqabalah, is ...

Hardy’s quote about Ramanujan, that “each of the positive integers was one of his personal friends”, aligns with Major’s interpretation of the Mayan head glyphs and other ways that people have imbued numbers with personalities. It suggests a deep, personal relationship with numbers, where each number is seen as a unique entity with its own characteristics and stories. Introducing these ideas to secondary math students could be beneficial. It could help to humanize mathematics and make it more relatable, fostering a deeper interest and engagement with the subject. Students could be encouraged to explore the stories and personalities behind other numbers, or even to come up with their own interpretations. This could be done through creative writing exercises, discussions, or research projects. In my personal perspective, the number ‘6’ is often seen as lucky, while the number ‘4’ is viewed as unlucky due to its pronunciation in Chinese, which is like the word for death. Moreover, Monday ...

It's surprising that the Roman numeral system was so deeply ingrained in medieval European education, even though it was cumbersome for mathematical calculations. Students and scholars continued to use Roman numerals, making arithmetic and advanced mathematical work more challenging and time-consuming. This persistence, in the face of more efficient systems, reflects the resistance to change and the preservation of tradition in educational approaches. The fact that the calculation of the date of Easter played such a central role in medieval arithmetic education is unexpected. The liturgical calendar heavily influenced the curriculum, demonstrating the profound integration of religion and education during that era. This ecclesiastical influence highlights the extent to which religious considerations shaped the content and structure of medieval European education. The declining emphasis on the quadrivium, which included arithmetic, as the universities grew is surprising. The shift to...

Two striking elements in the article were the active role of human agency in embodying mathematical proofs through dance and the profound influence of the natural environment on the choreographic process. The revelation that mathematicians became active agents in embodying mathematical proofs challenged the conventional notion of mathematical proofs as detached and objective. It emphasized the experiential nature of mathematics, underscoring that mathematics is something we actively engage with and embody. Additionally, the impact of the natural environment on the choreography highlighted the interconnectedness of mathematics, art, and the environment, showcasing the world as a powerful teacher and source of inspiration. These surprising aspects prompted a reevaluation of the boundaries and connections between mathematics, art, humanity, and the natural world. Incorporating the activity of dancing mathematical proofs, inspired by the approach discussed in the article, can be highly b...

Euclid and his work, "Elements," are still studied due to their foundational role in mathematics, timeless clarity, educational value, historical significance, and practical versatility. "Elements" sets a standard for precision, introducing rigorous definitions and deductive reasoning. It has served as a textbook for mathematical principles and proof, influencing generations. Its timeless principles and applications in areas like architecture and engineering keep it relevant. The historical impact and cultural significance of Euclidean geometry continue to inspire and educate, making it a vital part of mathematical tradition and education. There is a sense of beauty in Euclidean postulates, common notions, and principles for proofs. Beauty in mathematics often refers to simplicity, elegance, and harmony in the presentation of ideas. Euclidean geometry's postulates and principles exhibit a certain aesthetic appeal due to their clarity, logical structure, and th...

We delivered a group presentation that explored both ancient Babylonians and modern methods for identifying reduced Pythagorean triples, and we further delved into demonstrating the proof of the cosine law and its practical applications. My responsibility was to explore an extension of the Pythagorean triples, for which I chose the cosine law. I selected this topic because I believe it's a concept commonly taught and applied in secondary education. While I'm aware that the cosine law has numerous practical applications, I was still uncertain about which specific application to demonstrate in the class. Then, I recalled a news article I had seen in the past about the SFU cable car project, and it reminded me of a classic problem that involves both the Sine and Cosine Laws in determining the length of the cable. Due to time constraints, I only opted for this particular problem as part of the class activity. If time allows, I might consider selecting another problem that involves ...