Babylonian Algebra

Babylonians seems have been very creative in stating generalized mathematical principles. Their “place-value” number system and imaginative use of various tables are quite genius which allowed them to denote unknows before algebra time.  For example, ush refers to the length of an object, sag refers to the breath of an object, and sahar refers to the volume of an object.

Although these ancient mathematical representations were used to generalize mathematical concepts and calculation, it was also a reflection of how Babylonians’ great wisdom created a way to relate math with the nature world.  In my opinion, it was less abstractive and more relational to people’s daily life.

I cannot imagine how to find unknowns without the x, y symbols in modern day mathematics.  People are so used to what have today. Our ancestor’s legacy enabled us so much power to keep on advancing modern human world.  I find that the Babylonian’s way in manipulating mathematics is interesting and definitely applicable under the absence of the algebra.  I also believe if algebra wasn’t invented, human would have the wisdom to invent another system to serve for the same purpose.

 

 Babylonian Tables - Find Number 45 Using Base 60

I chose the numbers which are factors of 60,then I tried to multiply another number which makes the products 45. 

 

The Crest of the Peacock 

- A Unique Perspective on Ancient History of Mathematics 

The history of mathematics is fascinating and remains mysterious to us.  After reading the article, the “classic” Eurocentric trajectory seems untenable.  The alternative explanation for the development of ancient mathematics provides me a fresh look.  Under this new interpretation, the contemporary non-European mathematical activities have been ignored, devalued or distorted (Joseph, p. 3).  This unconventional view is sure to be controversial.  Some readers’ reviews on this book are quite negative and they claim the problem of Eurocentrism is overstated.

The second interesting point which attracts my attention is about Pythagoras. I don’t quite remember how many times I have heard Pythagorean theorem but never really investigated the story behind the theory.  Pythagoras, the ancient Greek thinker, in our modern world is famously known as mathematicians and cosmologist.  However, there is no evidence left for any of his work in mathematics or science.  In his days, Pythagoras was seen as an expert on the fate of the soul after death and religious ritual, according to Stanford Encyclopedia.

The third interesting point is how India played an important role in the transmission and diffusion of ideas in ancient history.  Particularly interesting to me is the cross-cultural contact between Indian and China.  Around the first century AD, Indian became the centre of pilgrimage of Chinese Buddhists, which opened the door for scientific and cultural exchange (Joseph, p. 16).

The unique perspective on mathematics from this book is attractive. I would love to read more in the near future.

 

Reference

Joseph, G. (2011). The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition). Princeton; Oxford: Princeton University Press.

 

 

 

 

 

 

 

 

 

Post 2

 

Why base 60?

One thing pops out of my mind is that one minute consists of 60 seconds and one hour consists of 60 minutes.  I guess base 60 relates to the revolution of the earth. When the earth rotates 360 degrees, sun rises and sun sets once which makes one day.  In addition, a circle has 360 degrees and until today we still use base 60 to tell time.  In Chinese zodiac, there are 12 animals and 5 elements (gold, wood, water, fire and earth).  Each animal has to rotate through each of the five elements to complete one zodiac cycle, which is 60 years.

Base 60 is also known as sexagesimal.  This numeral system was an invention of ancient Sumerians and was inherited by ancient Babylonians.  There are more factors of 60 than factors of 10.  Therefore, the base 60 system certainly has provided more convenience than base 10 system.  One thing interesting is that the Babylonians instead of using times tables, they did their multiplication by using a simple formula that depended on knowing just the squares and used it to compute the products of two integers (Gill,2019). However, the base 60 system wasn’t able to stand the test of time, but instead the base 10 system has dominated the numeral system. One important reason is because we have 10 fingers and much easier to count.

One interesting question is why base 20 was also very popular in ancient time?      

 

Reference

Gill, N.S. (2019). Babylonian Mathematics and the Base 60 System. ThoughtCo. Retrieved from https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679

 

 

 

Why teach math history?

Mathematics is one of the oldest scientific subjects which evolves along human history.  To study the history of mathematics allows me to understand how one specific mathematical concept was born, and how it was evolved over years in terms of format, notion, computational method etc.  The subject itself is dry, but with more historical stories and anecdotes introduced in class, I can make math teaching more fun and the students will develop more interest in it.  One of my favorite classroom anecdotes is the story of Gauss’s Arithmetic Sequences.  It was so fascinating to learn the story of a 9-year old’s smart observation rather than solely memorizing a dreary formula.  The history of mathematics provides me a space to connect, to imagine, and to appreciate all the wonderful human inventions.

In this week’s reading, there are several interesting points which draw my attention.  The authors talk about “genetic approach” which is to integrate the history component into math teaching.  This approach emphasizes less on how to use theories, methods and concepts, and more on why it provides an answer to specific mathematical problems and questions (Sierpinska 1991, p.11).    The point made here explains why many students had very high marks in math tests at secondary level, but later on had never pursued mathematics as major at university level.   When math was introduced, these students were able to develop perfect computational and tests skills, but lacked of skills in constructing crucial steps in thinking and making connections from the past to current.  Another interesting point is that role plays can be designed and implemented in mathematical teaching, although some argues that it is not mathematics.  However, to me, this is a valuable information and it could be used as one of my future teaching technics for sure.

The reading is an eye-opening piece.  It provides many essential and practical teaching pedagogies for prospective teachers.  For example, I could assign a small group project and let the students explore and investigate how one particular math theory was formed.  Let them answer the questions such as who the contributors were, when it was formulated, and how it was developed over time.  The ideas and examples introduced in this article such as historical snippets, historical based research projects, plays etc. have widened and solidified my understanding of classroom teaching.

Reference: 

Sierpinska, A. 1991. ‘Quelques idées sur la méthodologie de la recherche en didactique des

mathématiques, Iiée a la notion d’obstacle épisteéologique’, Cahiers de didactique des

mathématiques (Thessaloniki, Greece) 7, 1 1-28.