Comparing Number systems

It seems that the ancient Egyptian system uses more symbols than the Babylonian system. Also, we know more about what their symbols mean. It seemed with the Babylonian symbols it was just a variance of different tick marks but the Egyptian system had meaning behind the different symbols, perhaps connected to when this number was commonly used. I think the Babylonian symbols seemed easier to write than the more intricate symbols the Egyptians used such as the flower, or figure for 1 000 000. The Egyptian system seems closer to the base 10 system we use today. Roman numerals seem more similar to the Babylonian system in the sense that it's just tick marks at different angles but it is more similar to base 10, like the Egyptian system. 

Ancient Egyptian Surveying

1) I am curious how they decided the length from the elbow to the tip of the middle finger because that would differ for various people.

2) I am curious about the development of the ancient Egyptian approximation for pi.

It surprised me that there was a religious connection to surveying and the angles used for building the pyramids.

Russian Peasant Method for Multiplication

 

This method works because it converts it to binary multiplication. We need even numbers so whenever we have an odd number we ignore a group of whatever we were multiplying it by, so we have to add it to the end. 

Ideas taken from: https://mathcurious.com/2019/12/29/the-russian-multiplication-method/#:~:text=The%20Russian%20peasant%20multiplication%20method,multiplication%2C%20rather%20than%20base%2010.

Ancient Egyptian Multiplication & Division

 I attempted two problems, first 43x9 and then 87/5.

I enjoy the method for multiplication and find it easy to double so the process goes fairly quickly. With the division problem, I ended up with 17.5 instead of 17.4. I think this is because we "ignore" halves so we don't get the precise decimal. I tried it another way but I got 18. I think the division method does not work as well as the multiplication method likely because there was not necessarily an understanding of a system for irrational numbers or use of certain fractions.

Homework #1 09/20

Simple words were used instead of the notation we know today but the meaning really has remained the same. I sometimes think that the amount things have been abstracted is a detriment to students. Saying the side of a rectangle is "length" is much more clear than "x" and may be the best way to teach students when introducing the idea of unknown quantities. This reinforces the value of incorporating history into Math education because it gives meaning to the notation we use today. I do not agree with the statement that mathematics is all about generalization and abstraction. I think Math is much more artistic than trying to abstract and generalize and often Mathematics has been developed to solve a specific problem. It is "about" creative thinking and answering questions but has been abstracted in order to extend ideas. When thinking about geometries, without algebra there is a greater reliance on images and description. Thinking about multi-variable calculus I cannot imagine studying it without algebra. Here, abstraction was a tool in creative thinking but not the purpose of Math.

Homework #2 09/20

I had an assumption that a word problem that was not realistic in "real life" was an unhelpful word problem but looking at how they were used in the Babylonia era gave me an appreciation for problems that focus on 'pure' math. It shows that the people at that time had a concept of Mathematics as a "unified area of study" and were using abstracted word problems to implement the Mathematics they were practicing. Students want to have a reason for why they are learning a topic or solving a certain problem and I don't think the answer can always be that they will use it in real life. The idea of pure vs. applied mathematics does not rely on our familiarity with contemporary algebra because ancient civilizations were engaging with these two sides of Mathematics. I see the value in solving problems that focus on certain Mathematical skills and develop skills such as problem-solving, reasoning, logic or models.

Base 60 Practice

 4        9

6        7, 30

10        4, 30

12        3, 45

16        2, 48, 45

Babylonian number system

1) Perhaps 60 was a convenient base for the Babylonians because they measured something else in groups of 60. If a season was 60 days, perhaps it made sense for a different symbol to represent that quantity. 60 also has more factors than 10 and perhaps it made it easier to use or more straightforward to represent parts of a whole (60 being the whole).

2) As briefly discussed in class, we use 60's when talking about time. 60 seconds in a minute, 60 minutes in an hour. We know that half an hour is 30 minutes and a quarter is 15. The imperial system also fits better into 60's. 


3) Sexagesimal (base 60) numeral systems developed in different cultures. Some possible reasons include: that sixty is a highly composite number with twelve factors. Also, people counted to twelve on their fingers using the thumb to point to each finger bone on the four fingers. The strongest argument is that it was useful for writing and calculating fractions. It is also suggested that there were advantages to merchants and others doing financial transactions when there was bargaining and splitting up bigger quantities. 

Source: Asian, E. Babylonian mathematics. https://cloudflare-ipfs.com/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Sexagesimal.html

Christine - Crest of the Peacock introduction reflection

I was surprised to read how much different cultures interacted and likely shared Mathematical knowledge. It is interesting to me to read about where we get certain words and by extension the roots of mathematical knowledge. I did not know that the Arabs should be credited with the production and teaching of a substantial amount of mathematical learning. I am reminded again of the prevalence of the Euro-centric narrative of history and how my education neglected to teach the many developments in cultures outside of Europe. The transfer of technology, ideas and mathematical knowledge happened between many cultures. I also found it interesting to read about how place value was discovered independently at least four times; it fascinates me that humans in different parts of the world independently make the same discoveries!

Christine - Reflection: Integrating history of mathematics in the classroom

Before reading this article I had a lot of curiosity about Math history for my own interest but I did not assume it was overly relevant for high school students to learn. I believe teaching in context can be helpful and teaching Math in the context of how it is applicable today I think is a very effective way of presenting content. I had not considered that presenting concepts in the context of how they were developed could be another way of giving the information relevance.

I appreciated the perspective of history being a bridge of Math to other subjects. I look forward to learning more about Math in history to understand more of those contexts. I think there's value in showing students that Math wasn't developed in an isolated space but alongside other scientific and cultural questions. I question whether it is possible to integrate a lot of history into the Math classroom when there is so much material to cover. I think teaching Math in the context of how it is relevant today may be a more efficient way to bring relational understanding to the students. I think present-day connections may also be more interesting to many students. I connected with the idea that integrating history into Math education shows students that mistakes are a key part of the learning and discovery process. 

Having read this piece, I am interested in finding ways to incorporate history into my teaching and I can appreciate that it is a good method of putting the knowledge into a more relevant context.

hello world!

 Hi all! This is my first post.