Sijie Yang

  The most interesting part of his article is the creation of the stick charts as mattang that was used to explicate the principles of swell and land interaction. From my perspective, Marshallese mattgang, which is a simplification of a real-world system, visualizes refraction, reflection and diffraction of swells through geometrical ideas including perpendicular bisector, intersection, arc and so on. Marshallese wisdom is not only reflected in modeling the swell phenomenon with a certain purpose in mind, selectively eliminating some microscopial factors that have limited impact on the system, but also reflected in their teaching philosophy which emphasizes visual and kinesthetic information while training navigators - “in fact, one navigator recounted that an early part of his training was being made to float in the water at various places in order to learn how to feel what would later be shown and explained to him.” Embodied mathematics is significant in the history of mathematic...

In this assignment, I choose to talk about "a historical innovation that had mathematical implications." The innovation was a puzzle called Tangram invented in China. I will present it by creating a piece of art (Tangram) and express what I have learned from the interesting history of Tangram. Books: Demaine, E.D., Demaine, M.L., & Rodgers, T. (Eds.). (2008). A Lifetime of Puzzles (1st ed.). A K Peters/CRC Press. https://doi.org/10.1201/b10573 The article "Tangram: The World's First Puzzle Craze" in Chapter II "In Hindsight" depicts the craze of Chinese Tangram in Europe during 19th century. The article also shows many historical pictures of the earliest known Tangram and relevant merchants. Danesi, Marcel.  An Anthropology of Puzzles : The Role of Puzzles in the Origins and Evolution of Mind and Culture , Bloomsbury Publishing Plc, 2018.  ProQuest Ebook Central , https://ebookcentral.proquest.com/lib/ubc/detail.action?docID=5602778. Chapter 1 ...

  “Among the Greeks computation or reckoning, the arithmetic of business, was called logistic and was considered to be entirely different from the study of numbers as such, which philosophical study was called arithmetic” (page 266).    It is interesting to see that ancient Greek scholars have intentionally started to distinguish “applied mathematics” from “pure mathematics” by creating two different subjects called “logistic” and “arithmetic.” According to their standards, Euclid’s work The Elements which we studied in the history class is a representation of “arithmetic” because the content in the book is apparently not dealing with “sensible objects,” but rather a discussion of properties of numbers and proof.   “Throughout the Middle Ages, university instruction was based on a lecture-disputation method … There were no examinations in the modern sense of the term… To qualify for a degree, [the student] was required to participate in public disputations, either d...

Three characters are mentioned in Millay’s poem, Euclid, “Beauty” and “Praters.” In the first line of the poem, “Euclid alone has looked on Beauty bare” while other praters are still pondering the secret of Beauty. It is tempting to think that “Beauty” is mathematics, meanwhile the word “bare” is equivalent to the word “pure,” “intrinsic” or “minimalistic.” Even though the beauty people see is “in shapes of shifting lineage,” meaning mathematics is being discovered, perceived and interpreted differently by different people, Euclid is the only person who saw the very cardinal rationale of mathematics; he “anatomized” mathematical problems and proved them based on the postulates and axioms. In his work The Elements, He did not only discover the beauty of mathematics, but also proved them beautifully with the simplest mathematical language.      After walking through the biography of Euclid and analysis of his work, I begin to understand why his work has been so popular for ...

In the video, the dancer and mathematical choreographer, Samuel J. Milner, provides an insightful thought on why we want to embed aesthetics, especially artistic choreography, into mathematics: “When you see it on the page, it’s all there at once. But when you go through it mentally, you need to go through it step by step. So doing it as a dance, which takes time, somehow makes a little bit more mental sense… [1]” Back to the ancient time, the process of establishing the truth of a mathematical statement is torturous but exciting. Designing the dances to recreate and visualize those hot inventions is a valuable opportunity for our students to dissect the process of proofs step by step. Dances anthropomorphize mathematical ideas and make rigid proofs more vivid and memorable.  Moreover, the article written by Samuel J. Milner, Carolina Azul Duque and Suan Gerofsky also bring out an innovative platform on which we can meld land-based learning and decolonization with mathematics ...

If we acknowledge non-European sources of mathematics, students will have more opportunities to be exposed to various approaches of solving or proving a mathematical topic. The article "Was Pythagoras Chinese - Revisiting an Old Debate" shows us the Chinese-version proof of the a2+b2=c2 relationship. The proof that is exhibited by Zhoubi suanjing  is different from the rigorous proof in The Elements and can be easily understood by students. Inspired by the method, students can learn how prove a geometric theorem with the help of grid. The article also demonstrates Chinese approaches to calculate the accuracy of π, which can be utilized when we teach the topic of circle in mathematics class. By looking at various methods developed by various civilizations can also enrich students' problem-solving techniques and broaden their views in the journey of mathematical study. The Crest of the Peacock: Non-European Roots of Mathematics  written by George Gheverghese Joseph has...