Ian EDCP 442 2020

  While the use of algebra, or the use of single letters to represent unknown quantity, makes problem solving easier to present and understand, I think it is not strictly necessary to do so in order to state anything mathematically precise. For instance, I can state Pythagorean’s theorem as the sum of the square of the two shorter side lengths in a right-angled triangle is equal to the square of the longest side length of the same triangle. This would be more compactly represented using a diagram and labelling the sides with letters like a,b,c as commonly done. Using words specific in language to represent math might bring trouble when communicating with others outside of your region, but perhaps that wasn’t a problem when people were mostly confined to their local region without effective transportation.   As for whether math is all about abstractions and generalization, I would say that abstraction is a tool that allows people to work on problems presented to them withou...

1 45 2 22,30 3 15 4 11,15 5 9 6 7,30 10 4,30

Upon my initial reading of this book, I am surprised by the Eurocentric presentation provided in figure 1.1. The figure attributes development of mathematics solely to Greeks and Europe. I am simply surprised that this was the kind of “facts” put into textbooks in European countries. I myself attended school in Asia for the early years of my childhood, and it was definitely not presented that way. I am Chinese, and while there was not an emphasis on history of mathematics in China, I know that China has a long winding history and developed many mathematical ideas independently from the west as there was little communication. Things like arithmetic, number system, Chinese Remainder Theorem are all notable examples, and there are recovered books and documents showing many mathematical ideas such as taxes, percentage, division, even measurements of pi, volume, area…etc. So drawing from my own experiences, the Eurocentric presentation is a shock. The second interesting point for me is ...

  Why is 60 convenient? My guess is that 60 is larger than 10, and a large number can be expressed in base 60 with significantly less digits in a base 60 system compared to a base 10 system. Since much of the math was done on clay with wedge shaped markings, putting less markings was likely easier to do and less prone to error. Just like it would be painful to use base 2 in everyday life by placing many 1s and 0s, using wedge shaped markings to put down many digits was likely a difficult task. Also, the number 60 has many divisors, namely 2,3,4,5,6,10,12,15,20,30. Compared to 10, which is only divisible by 2 and 5,it might be easier to group things in multiples of the above divisors to quickly count. We still see 60s in some measurement units. The first one that comes to mind is time in seconds and minutes and hours. 1 minute is 60 seconds and 1 hour is 60 seconds. This aligns perfectly with a base 60 system, since 1 hour is 3600 seconds which might be hard to remember but as ...