## Combinatorial Sets from East Asia

**By: Tao Steven Zheng**

This article introduces sets of abstract figures found in East Asia that are pictorial representations of combinatorics. These diagrams were probably conceived without the intent of being mathematical, but ended up being mathematical curiosities in modern times.

The 64 hexagrams of the *I-Ching* or *Yijing* (易經) is
the foundation of an ancient Chinese form of divination that dates
from the Western Zhou dynasty (c. 1050 - 771 BCE). Each of the 64
hexagrams is a combination of six bars. The solid bar represents
*yang* (陽), the positive force. The broken bars represent
*yin* (陰), the negative force. Interestingly, the sixty-four
hexagrams can represent the set of binary numbers from 0 to 63.

The math behind the I-Ching hexagrams is simple. …

## Test

The ubiquity of

Hey, it works. :)

On a side note, I need a little bit of help for those that knows LaTeX. When on each line of code when you want to separated different sentences. The first word of the second sentence always is a few spaces further then the first word on the first sentence. Why's that? And how do I fix it?

So for example: Similarly, we can...

Thus,
...

## Chinese Derivation of Pythagorean Triples?

**By: Tao Steven Zheng**

In the Chinese mathematical text *Jiuzhang Suanshu*, we
find an interesting problem that requires the Pythagorean triples
formula to solve.

**Chapter 9: Gougu Problem 14**

今有二人同所立。甲行率七，乙行率三。乙東行。甲南行十步而邪東北與乙會。問甲乙行各幾何？

[There are two persons standing at the same location. Person A moves at a speed of 7. Person B moves at a speed of 3. Person B moves east. Person A first moves 10 bu south, then diagonally northeast until he meets person B once more. How far did each man travel?]

- bu (步) literally means pace, a Chinese unit of length that measures roughly 1.6 meters long.

The units of the speed are not specified, but it is reasonable to assume that the speed is measured in bu per second, which measures 1.6 meters per second.

For calculati…

## Ancient Chinese Mathematics (1600 BC - 600 AD)

**By: Tao Steven Zheng**

- 1
**Note to the reader** - 2
**Section 1: Early Antiquity**- 2.1
**Mathematics of the Shang** - 2.2
**Mathematics of the Western Zhou** - 2.3
**Mathematics of the Eastern Zhou**

- 2.1
- 3
**Section 2: The Early Imperial Age**- 3.1
**The Math-deprived Qin?** - 3.2
**Mathematics of the Han**

- 3.1
- 4
**Section 3: Era of Disunity**- 4.1
**Liu Hui** - 4.2
**Sunzi Suanjing**

- 4.1

This historical overview on the mathematics of ancient China includes the major developments of mathematical thought in ancient China from the Shang dynasty (1600 – 1046 BC) to the Northern and Southern dynasties (420 – 589 AD). The mathematical development from the Sui dynasty (589 – 618 AD) to the Qing dynasty (1644 – 1911 AD) would be considered Medieval Chinese mathematics, and will not be discussed in this article.

Much of Chinese mathematics…

## Timeline of Chinese Mathematics

]] **1811 – 1882 AD:** Li Shanlan develops transcendental
functions, infinite series, and combinatorics from ancient Chinese
mathematics

## Mathematics from Far East Asia: An Interactive Timeline

**By: Tao Steven Zheng**

Click here to view the interactive timeline.

Enjoy this video of a Song dynasty mechanical clock tower!

## Intro to the Abacus

**By: Tao Steven Zheng**

There is a growing epidemic of **dyscalculia** among today’s
youth. The over-reliance of electronic calculators has led many to
add and subtract slowly, forget their multiplication table, and
fail to search for divisible factors. The abacus is an ancient
computation tool that can remedy this modern malaise. How? Well,
the abacus is just a tool that speeds up computation, but the
computation is still done by the human brain. It trains the brain
to think faster and more strategically. It internalizes the
**decimal number system**. It requires the user to memorize the
multiplication table, and the factors of a given integer.

Abacuses have been invented by several cultures around the globe; at different times. Many early abacuses were …

## Zheng's Problem Solving Process

There are five steps to problem solving:

1) understanding

2) organization

3) strategy

4) execution

5) reflection

**Step 1: Picture the problem (Understanding)**

Read the problem carefully to know what is known and what is not known. Understand the objective of the problem. Write down what is known and what needs to be solved.

**Step 2: Get organized (Organization)**

Separate the relevant and irrelevant parts of the presented information, and eliminate the irrelevant information. Translate words into the mathematical language. Introduce variables for the unknown quantities discussed. Attempt to obtain more information from prior knowledge, or by dabbling with the information given in the problem. Make correct connections between the gathered information i…

## Math Book Reviews by Steven Zheng

- 1
**Elementary Number Theory in Nine Chapters****(Second Ed.)** - 2
**Explorations in Geometry** - 3
**Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last 10 Centuries** - 4
**How to Solve It** - 5
**A History of Chinese Mathematics** - 6
**Janos Bolyai: Non-Euclidean Geometry and the Nature of Space**

**Author:** James J. Tattersall

Rating: 10/10

This is an excellent (and readable) intro text to number theory with proofs to many important number-theoretic formulas and theorems. Aside from theory, there is also an emphasis on applications such as calendrics, representations, and cryptography. From front to back, there are many interesting historical notes that connect the subject to several cultures (including Chinese, Muslim and Indian). I highly recommend t…