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Showing posts from September, 2019

History of Babylonian Word Problems

After reading the assigned piece, I wondered how effective and efficient the usage of these word problems was. In a historical sense, when looking at what resources were available at that time, I can understand why they used the methods that they did, however, in today's context, it doesn't make much sense. When actually looking at the problems, there are a lot of numbers with many fractions, I wondered why they couldn't use easily divisible numbers. I think that these problems help people visualize mathematics and view them in a more realistic perspective. I think this can be extremely helpful in teaching mathematics, and making solving problems fun for the solver. Doing word problems also involve a lot of creativity when solving, I think that this can build up and help someone become a more creative thinker. One benefit with these word problems is that they work on both English and mathematics skills, in order to solve the problem, you must first be able to comprehen...

Word Problem using Unit Fractions

A man who had 12 horses and 3 children wrote in his will to leave 1/2 of his horses to Pat, 1/3 to Chris, and 1/12 to Sam. However, just after he died, one of his horses died too. How will the children divide the 11 remaining horses in order to follow the instructions of the will? There were twelve horses that should be given to the man’s children; one half of twelve horses, that is six, to Pat, one third of twelve horses, that is four, to Chris, and one twelfth of twelve horses to Sam. The total number of horses distributed to the children is eleven, because 6 + 4 + 1 = 11. Therefore, although one horse died, the children will have no issue inheriting horses to follow the instruction of the will. We can use unit fractions when dividing up things that don’t divide cleanly (ie. have lots of decimals). We can use fractions to avoid these long numbers. I do think that the benefits havent changed much from back then, the outcome is the same we just have different ways of reac...

Babylonian Algebra

When comparing our algebra to the Babylonian algebra, there are some very noticeable differences. The very first thing that I noticed when looking at the Babylonian algebraic methods was their use of variables, and what they called their variables. Instead of using "X" to describe length, they would use "ush", instead of using "Y" to describe breadth, they would use "sag". Another thing that I noticed was their notiation when solving quadratic equations. I found this to be quite interesting especially because of the way we have all been taught to solve these types of equations. It's crazy to think that these people were able to solve quadratic expressions using a method that is not the one we have been taught in modern society. I think that generalization and abstraction do play a large role in mathematics, however, in order to excel in mathematics, it takes an individual with a certain amount of problem-solving ability rather than generaliza...

Base 60 Multiplication Table for 45

Column I           Column II 2                       22,30 4                       11,15 5                       9 6                       7,30 12                     3,45 20                     2,15 30                     1,30

Three Suprises from Introduction to Math History

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After reading Crest of the Peacock by George Joseph, there were three things that I found to be quite surprising. When I first began reading the introduction, I really didn't have a great idea about math history, other than the Babylonian base 60 system that we had covered last week. One of the first things I was surprised by was the great impact that India had on the evolution of mathematics throughout history. It was stated in this piece that Indian and Arab influences have had a hand in helping to further mathematics and teaching mathematics. Another thing that I found surprising was how information about mathematics was shared between countries. I found this very surprising since they didn't have telephones or the internet back then so it was very hard to spread information and communicate with other people from different countries. The communication between European and Middle Eastern nations really helped further the entire world's understanding of mathematics and pla...

Why Babylon used the 60 number base system

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When doing the in-class exercise analyzing the Babylonian mathematics system, I was initially very confused about what the different symbols they used represented. However, after spending some time looking at the symbols and comparing them to the next multiple, I found out that they used a base-60 system. I wondered why they did this, as a base 10 system seemed much simpler to me, so I decided to do some research on it. I found out that this was likely due to the fact that there are 5 fingers on one hand and five multiplied by twelve equals sixty. I think that the number sixty is special because it has twelve factors compared to ten which has 3, therefore it has more divisors. Sixty is significant for many things in our daily lives, but especially for how we keep time. It is a good number to use for time-keeping and many other things because of the number of divisors it has. I never really noticed our usage of the number 60, but doing this exercise has opened my eyes to exactly how m...

Integrating History in Math

Throughout elementary and high school I had never wondered about the origins of mathematics, even though I have been doing mathematics as long as I can remember. I think that it is very important for young students to learn about the origins of mathematics, as it will help them with understanding why exactly they are being taught it. I feel as though the origins of mathematics should be taught as apart of history class, along with Babylon and Mesopotamia. It is important for students to understand why they are learning concepts and I believe that being taught the history of mathematics will achieve this. I also think that it would be very interesting to see the methods used by people in the past, like how they made transactions, how they collected payments, etc. Learning these things would help keep students engaged and help them understand why they are doing mathematics and it's importance in history. Something that stood out to me in the article was a few of the ideas and exa...