Mathematics in Ancient China

Decimal System:   Fourteenth Century BCE

The decimal system originated in China and was used for thousands of years before western civilization began using the same base 10 number system. The earliest records of the Chinese using the decimal system was to represent dates, where one inspection wrote ‘547’ as ‘five hundred plus four decades plus seven of days.’ A probable explanation for such early usage of a base 10 number system is that the Chinese wrote in characters instead of using the alphabet, so there wasn’t the same temptation to give '10' its own symbol and so forth. The decimal system appeared centuries later in much of the world where it has become a fundemal piece of modern science.

Negative Numbers:   Second Century BCE

Negative numbers were once a very difficult concept to accept for the western world. Ancient mathematicians found the idea of negative numbers absurd and not applicable to mathematics or everyday life. China was centuries ahead as negative numbers were ingrained in their mathematics. They could be seen on counting boards where rods were either black or in the shape of the square. The rest of the world was making great progress in mathematics, but it would take many years before they accepted negative numbers.

Pascals Triangle:   Eleventh Century CE

Pascals triangle is a triangular array of numbers that contains many different patterns which arise in mathematical fields such as probability theory, combinatorics, and algebra. Each element of the triangle is the sum of the element above and to the right and the element above and to the left. Pascal's triangle can be used to find the coefficients of binomial expansions, sequences of the fibonacci sequence, combinations (n choose k), and much more. The incredible mathematical pattern was not discovered by Blaise Pascal in 1623, but rather Liu Ju-Hseih more than 400 years before. The earliest depictions of the triangle come from a Chinese book written of 1303 but it was known in China by the twelfth century.