Babylonian Algebra from Crest of the Peacock

 Babylonian algebra is a really interesting concept for me to get my head around, because it took place so long ago! I am really impressed with how far the Babylonian peoples got in the development of mathematics, and their understanding of algebra. It is really interesting to recognize the similarities in the algebra that we use today.

I thought table 4.2 in the text was really interesting, as the Babylonians used words rather than alphanumeric variables in their word problems. I guess the Babylonian people had chosen to just use words to express their geometric terms, perhaps "simplifying" mathematics by using everyday words in their problems? 

I imagine it would have been difficult to generalize a mathematic principle without the algebraic notation. The Babylonians used words to generalize their mathematics, which makes me think that they had a deep understanding of principles, perhaps by relating it to everyday life? This reminds me of solving word problems in elementary school, where the problems were very simplified and applied to the real world (such as using pie or cake to understand fractions!)

Since algebraic notation and alphanumerical variables are so prominent in our understanding of mathematics, I find it really hard to comprehend how I would state a generalization without algebra. I can understand simple geometry and graph theory being explained with objects/visuals, but I really cannot imagine learning a generalized concept such as the quotient rule in differential calculus using words. I am really curious to look more into the Babylonian's development of mathematics after this reading!

Babylonian Style Base 60 Multiplication Table

Blogpost #3: Crest of the Peacock

This reading was highly interesting to me because I do not know much about the origins of mathematics and how it developed. There were quite a few things that surprised me, so here are the top three:

1. It was really interesting to me that there is such a favoured, dominant Eurocentric view when considering mathematics. Evidence actually shows that mathematics was developed between 800 and 500 BC by early Indians which they contained in the Sulbasultras. This was around the same time that the early Greek mathematics was recorded, which means that two different groups of people discovered and developed mathematics separately. In terms of history, our traditional upbringing has always been focused on a Eurocentric view. I really enjoyed that this reading challenged that norm and questioned whether or not our history was accurate. 

2. I did not know that science originated in China and India, and then was translated, refined, and distributed by Arab scholars. This was described as an Arab Renaissance of mathematics, which took place during the dark ages in Europe. It is important to note here that the Arabs played a crucial role in the spread and teachings of mathematics to Europe, which is not always acknowledged. Again, the Eurocentric view of history that we are all familiar with taints this narrative of the innovation and discovery that was actually happening among other nations. 

3. Towards the end of the chapter, the author highlights the flow of technology that originated from China in the 15th and 16th centuries. I found this particularly interesting because we still use many of these items today, such as the wheelbarrow, the crossbow, gun powder, the magnetic compass, paper and printing, and porcelain. I never knew that all of these significant items in our life were developed in China and then shared with the European world! 

Blogpost #2: Base 60

 Speculative Phase:

When I think of a possible reason as to why the Babylonians used base 60 compared to base 10, I think of time. I'm not actually sure without research if the Babylonian era was aware of there being 60 seconds in a minute, and 60 minutes in 1 hour, but this would make the most logical sense as to their use of base 60 for the notational system.

I came to this conclusion because this is how we measure time around the world. Scientists have been able to measure and establish a time system that revolves around base 60. In my opinion, 60 is still a significant number in our current lives because of its correlation with time, and it is interesting to think about how the world would be if we adopted a similar notation system with base 60. After considering the Babylonian system, I am actually curious to why we adopted the current notational system with base 10?

Research Phase:

After doing a bit of research, it appears that the Babylonian numeration system using base 60 actually aroused through trade. It appears that the Babylonian numeration system is based off of the Sumerian system, which involved two different groups of people merging together. One group had a number system based on 5, and another based on 12. So when the two groups traded, they multiplied their systems to establish a more universal system based on 60. 

I found this information through this article, which was a very interesting read! 

link: https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679

Something I found particularly interesting about the use of base 60 is its divisibility. 60 is a composite number that has 12 factors, so fractions are easier to understand because they are simplified. 60 is actually the smallest number that is divisible by every number from 1 to 6, as 1 hour can be divided into 30 mins, 20 mins, 15 mins, etc. Discussing this system and looking into the number 60 makes me think that this could be a useful alternative approach to teaching young kids about math. Since 60 is a significant number correlated with time, and time is such a relevant topic in our lives, I think it would be interesting to teach young students about the Babylonian techniques and tie that to lessons about division and fractions. It may be easier for kids to grasp, as well as still effective in teaching them fundamental lessons in math! 

Blog Post 1: Why Teach Math History?

    As a commerce student, I come across math quite frequently in my core classes and prerequisites. Throughout my degree, and even before that as a high school student, I have never considered the possibility of learning math history. I was very curious to take this class because I do believe that incorporating historical contexts on the math that we learn can actually make it a lot more interesting. I can imagine that learning the origins of the finance formulas that I use day to day can actually give me a deeper appreciation for the discipline itself. 

    I think many people, especially students, typically just do what they are told to do, and complete their math problems to satisfy requirements. After reading this thought-provoking article, I do believe that incorporating the origins and history of the mathematical concepts we learn in class can help spark interest in the subject itself. I believe math is a misunderstood subject, that is characterized by being difficult and boring. Although we haven’t gotten into learning about the origins that derived from ancient civilizations, I do think that sharing these stories would help students understand how the math they are learning today developed. I think that may be interesting for them, because personally I am always intrigued by the “why”. “Why” are we learning this? I think the integration of mathematics history can help students come to their own understanding of “why” this is important for them to learn. 

    Another interesting point that this article highlighted is the human endeavour that is portrayed when studying mathematics history. I particularly agree that studying the history of mathematics can distinguish that “mathematics is an evolving and human subject rather than a system of rigid truths.” Students may not be able to understand this philosophy of math by being taught rigorous analytical concepts. I agree that teaching the historical contexts may give math some humanity. Overall, I really enjoyed this article because it offers some very valuable techniques for an approach to integrating mathematics history. After reading this article, I now have more ideas and a deeper understanding of why incorporating history would be integral to student’s learning. 

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 Hi this is my EDCP 442 blog!