Counting
Chips, also known as counting chips, are a kind of calculating tool in ancient times. The digits of hundreds, thousands and tens of thousands have appeared in the oracle bone inscriptions of the Shang Dynasty. The Book of Songs Zhou Song Fengnian also mentioned that the grain harvest had reached trillions and zi. In the Zhou Dynasty, 100,000 was 100 million, and 1 billion was zi. Such a huge number was difficult to accumulate accurately without calculating tools at that time. Chips are made of wood, bamboo, bone, ivory, and even lead. They are usually round sticks. The earliest counting chips seen so far are bamboo chips unearthed from the Warring States wooden coffin tomb in Zuojiagongshan, Changsha, Hunan. In the Western Han Dynasty, ivory counting chips and metal (lead) counting chips were also unearthed in tombs. A set of counting chips has 271 pieces. Usually each piece is about 13 to 14 cm long and about 0.23 cm in diameter. After the Han Dynasty, counting chips gradually shortened to 10 to 11 cm to facilitate calculation. According to research by Chinese mathematicians, in addition to the four arithmetic operations of addition, subtraction, multiplication and division, ancient counting rods can also solve square roots, cube roots and even multivariate high-order equations. The book "Records of Mathematics and Art" written in the Northern Zhou Dynasty lists 14 ancient calculation methods, including abacus calculation, which is faster than counting rods. In the Song Dynasty, abacus calculation was improved to abacus, which completely replaced counting rods. In the article "Night Reading and Picking Up Records (84) Planning in the Curtain, Deciding Victory Thousands of Miles Away", it is mentioned that Zhang Liang borrowed Liu Bang's chopsticks as counting rods, and spoke for Liu Bang one by one, counting Li Sheng's bad ideas one by one. Sometimes, people also use fingers to count, which is equivalent to using fingers as counting rods. This kind of calculation is all 1+1+1+1. If counting rods are used, horizontal and vertical chips can be used to arrange one to nine odd numbers, and moving one digit to ten, two digits to hundreds, and three digits to thousands, the position is also very clear. (No pictures available, please provide them.) (No pictures available, please provide them.)