By: Tao Steven Zheng (郑涛)
Large Numbers
During the Spring-Autumn and Warring States period (771 – 221 BC), the large numbers above “ten thousand” (万wan) were expressed as powers of ten. After the Han Dynasty, the large numbers above “ten thousand” were expressed as powers of ten thousand. According to the first chapter of the Sunzi Suanjing:
凡大数之法,万万曰亿,万万亿曰兆,万万兆曰京,万万京曰陔,万万陔曰秭,万万秭曰壤,万万壤曰沟,万万沟曰涧,万万涧日正,万万正曰载。 | The rule of large numbers states: wan-wan is called yi (亿), wan-wan-yi is called zhao (兆), wan-wan-zhao is called jing (京), wan-wan-jing is called hai (陔), wan-wan-hai is called zi (秭), wan-wan-zi is called rang (壤), wan-wan-rang is called gou (沟), wan-wan-gou is jian (涧), wan-wan-jian is called zheng (正), wan-wan-zheng is called zai (载). |
Number | Description in the Sunzi Suanjing | Value in the Sunzi Suanjing |
万wan | 104 | 104 |
亿 yi | 104104 | 108 |
兆 zhao | 104104108 | 1016 |
京 jing | 1041041016 | 1024 |
垓 gai | 1041041024 | 1032 |
秭 zi | 1041041032 | 1040 |
壤 rang | 1041041040 | 1048 |
沟 gou | 1041041048 | 1056 |
涧 jian | 1041041056 | 1064 |
正 zheng | 1041041064 | 1072 |
Problem Study 1: Nine Dykes
The following problem is from the Sunzi Suanjing (Chapter 3, Problem 34).
今有出门望见九堤。堤有九木,木有九枝,枝有九巢,巢有九禽,禽有九雏,雏有九毛,毛有九色。问:各几何?
术曰:置九堤,以九乘之,得木之数。又以九乘之,得枝之数。又以九乘之,得巢之数。又以九乘之,得禽之数。又以九乘之,得雏之数。又以九乘之,得毛之敷。又以九乘之,得色之数。
|
Suppose that after leaving a town gate, one sees 9 dykes. There are 9 trees on each dike, 9 branches on each tree, 9 nests on each branch, 9 birds in each nest, 9 fledglings per bird, 9 feathers on each fledgling, and 9 (different) colours on each feather. Question: How many are there of each?
|