History of Chinese Mathematics

Chinese mathematics started to emerge in the 11oo BCE.  They discovered many important topics including negative numbers, decimals, and trigonometry.  It is difficult however to find information prior to 254 BCE, but the limited information we have will be where we start our journey through Chinese mathematics.

We first look at the Shang Dynasty and the Yi Jing.  This book influenced later work in the Zhou Dynasty.  The Yi Jing, or the I Ching, showed the uses of the hexagram in mathematics and contains one of the first uses of binary numbers.  The book also showed that the Chinese had a basic understanding of equations and negative numbers.  After the Shang Dynast, the Zhou Dynasty showed the importance of mathematics in society.  This is best presented in the idea that math was one of the Six Arts that students were required to perfect.  The perfect Chinese student that learned the Six Arts could be equivocated to the Renaissance Man in western Europe.

Even though math was seen as important during the Zhou Dynasty, we see a backwards slide during the Qin Dynasty.  This is because Emperor Qin killed academics in droves because he wanted to change the cultural dynamics of the country to one of subservient peasants; however, one mathematical idea that left the Qin Dynasty was the standardization of weights, which allowed for easier trade.  Furthermore, there is evidence that the Chinese understood advance formulas for volume and proportions because of the architectural wonders produced during this time.

Math makes a comeback during the Han Dynasty.  This is best seen in the way of the discovery of putting numbers into a place value decimal system.  Furthermore, they had a concept of the number zero in the form of leaving a blank in the counting board to mean zero.  Finally, Zhang Heng gave the most accurate approximation of pi up to that point in Chinese history.

The final dynasty we will look at is the Tang Dynasty.  This is because by the Tang Dynasty rolled around mathematics was a standard subject; so much so that the use of The Ten Computational Canons was used regularly.  This was a collection of mathematical works put together by Li Chunfeng and was used as the official textbook for the imperial examination.  Another important thing was that the cubic equation appeared for the first time with Jigu Suanjing.  Finally, they had a practical understanding of plane trigonometry with regards to the sine, tangent, and secant values.

As we can see, mathematics flourished in China without the help of the western powers. It can even be said that it was developed independently from the Europeans.  This is significant because the American education system only looks at the development of mathematics from an eurocentric perspective instead of a global perspective.  This just shows that a global perspective is necessary to completely understand mathematics.

Creating Tessellations

Making a tessellation is not difficult, but making them look interesting is.  To make a tessellation, we must take geometric shapes and combine them in a pattern where there is no overlaps or gaps.  Furthermore, the pattern must be repeating constantly.  A basic tessellation would be similar to the one found below:

 

This is more basic because it takes a simple hexagon and makes glide reflections to create a pattern.  A more advance looking tessellation would be something like this:

This is more advance because no matter which way we turn the tessellation, we see the same design.  Tessellations are beautiful pieces of art, but take along time to create.  This is why they are so highly valued by people.

What is an Axiom?

The definition of an axiom according to the dictionary is, “a statement or proposition that is regarded as being established, accepted, or self-evidently true.”  In mathematics, we add the stipulation that is the basis for an argument.  This means that we can build any argument we want as long as we start with the most basic axioms.

This is what Euclid did when he discovered Euclidean geometry.  He started with five axioms, and built an entire geometry dependent on them.  These axioms are so fragile that if one was shown to be inherently false, then the entire geometry would fall apart and work spanning over a hundred years would be meaningless.  This is because they all rely on the same basic “self-evident” truths.

Axioms are also seen in other parts of mathematics.  They are the building blocks of Algebra, Analysis, and Topology.  Without a basis for each of these mathematics, we as humans could not further these fields.  Without the axiomatic definitions of algebraic structures, we could not classify different sets into types of groups or rings.  These are universally given simply because we have decided that they are true.

Overall, axioms are little more than a way for humans to have a launching point to further our understanding of mathematical topics.  We have established them to be true simply to have almost a safety net of ideas that we can always fall back on.

What is Math?

Many people believe that math is just a series of convoluted equations that culminate in a single numerical answer, and the work was designed to confuse them.  On many occasions, I’ve had to defend why I would ever want to be a math major.  The reason is because math is so much more than equations.  The equations allow us to understand the relationships in the natural world around us.  Math is the study of relationships that many people take for granted.

1) Ancient Geometry: Before Euclidean geometry was found, many ancient civilizations had their own version of geometry.  Take the Ancient Egyptians.  Without their rudimentary understanding of shapes, we would not have the Great Pyramids or the Sphinx.  Without math, many of the wonders of the world would not have been built.

2) Calculus: This has allowed us to have cars and planes.  This is because calculus allows us to understand the relationship of speed, velocity, position, and acceleration.

3) Differential Equations:  These have allowed people to study the growth patterns of populations, which in turn allows people to recognize what resources are needed in order to continue.

4) Non-Euclidean Geometry: The finding of hyperbolic and elliptic geometries shows growth and development.  Just as the world evolves, so does math, but it is only because we finally are advance enough to find it.  All math is already there, but finding it shows that humans are developing into a more prestigious group.

Math is more than numbers.  Math is a timeline of human history that shows us how far we have come.