Re: Babylonian ‘algebra’ from Crest of the Peacock

 I think using algebra or single letter notation in math helpes solving problems in a much easier fashion and also easier to present and understand. However, I don't think it's necessarily a must in terms of solving math problems, a lot of math questions can be represented in words. So why do we have all the notations that we are using now? From the book Crest of the Peacock, we know that the fundamentals of mathematics were gathered from different countries/regions, in order for them to communicate notations had to be invented/created. It made more sense if the communication of math only happens in the same region, but communicating with others from outside the region might bring confusing. I would rather think of notations as the "regulations" for the math world. It's a universal tools for people to communicate in mathematical language at a ease. 

As for whether math is all about abstractions and generalization, I don't agree with that. As the concept of math is so broad and everyone learns/understands math differently. However, I do think abstraction is a great tool for students to ease into math as it gives the students the freedom to potray math as they like. Generilzation is also important as it gives the students some foundations/facts to imply math in a abstract way. Both are curial in math learning. 

I think using pictures/illustration would be a good way to state some math problems like geometry, or easy number theories. Stating calculus without algebra would be very hard. I still think notation's excitence has its purpose there. 

Re:Create your own Babylonian-style base 60 multiplication table for the number forty-five

knowing the example 2   22,30 with base 60, I then worked backward. setting the column 1 number first and I can then find combinations numbers for column 2. 

For example, I picked 4 as my column 1 number, so I know that column 2 must be (a+b/60)=45/4, since it's a base 60 question, it will be easier to change the base 45 to 60 which gives us 45/4=675/60. Simplify 675/60, gives us (11+15/60), therefore we have the answer of [4.  11 15]. Please see the below answer by using the same method. 

Re: The Crest of the Peacock by George Joseph

 

Three things that surprised me: 

1. The most significant developed mathematical activities was flourished around the twin rivers. It's so interesting to see how geography had a huge impact on how people's migration which leads to the rise of the economy in a certain area. Advanced mathematical development encourages the growth of the local economy and a growing economy also has a positive influence on the evolution of mathematics. 

2. I'm surprised that "by the second half of the first millennium AD, the most important contacts for the future development of mathematics were those between India and the Arab world." It's interesting to see that a lot of ancient math developments started in Asia and the Middle East. Maybe it's because of the silk road. Every culture has its mathematical history, but surprisingly they all have some common understanding/knowledge of numbers. 

3. I noticed that a lot of philosophers were involved in the revolution of math in history. It's interesting to see how math is not only related to numbers back then. Math is the product of the economy, philosophy, and astrometry, etc. That made me think that math is the foundation of a lot of things/subjects. I also find it's fascinating how Asian countries consider math is the most important subject in schools! Pure math might be boring, but reading about history and doing some researches might encourage students to take a like in this most-disliked course among high school students. 

Re: Homework to be posted by Monday, Sept. 21 at 9 AM on your individual blog: Base 60

I think the reason why 60 might be a convenient, significant, or especially useful number to use as the base for a number notational system is related to how we count time. 1 hour consists of 60 mins and 1-minute consists of 60 seconds and also 6 o'clock divides the clock/circle perfectly into 2 halves. In many ancient countries, 6 and 9 two magic numbers, especially 6 is considered as a number with peace and balance. When we think about time, a year has 12 months which is 2 times 6 as well. 

Surprisedly, we still have 60 seconds in 1 minute and 60 minutes in 1 hour! Seems like how we record time never really changed. In many cultures, there are still a lot of traditions that have close relationships with number 6, or 60. The Chinese zodiac has 12 animal symbols, and so as western horoscopes! When you think about the reasoning behind it, time was pretty much the only common knowledge/understanding of people across the world know despite different languages were spoken. 

After doing some research, the reason why Babylonian mathematics had a base 60 rather than 10 is that 60 has more divisors than any smaller positive integer which is so fascinating. Scientists even found out that they knew the formula that's today known as the Pythagorean theorem. Talking about the history behind 6, there was this "most commonly accepted theory holds that two earlier peoples merged and formed the Sumerians," USA Today reported. "Supposedly, one group based their number system on 5 and the other on 12. When the two groups traded together, they evolved a system based on 60 so both could understand it." Knowing the history behind all this really made me think about how math was created among people all around the world and it was serving such important purposes in people's lives.