Technique de la multiplication en Chine antique

Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were increasingly replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention of polynomial equations of up to four unknowns in the work of Zhu Shijie. The basic equipment for carrying out rod calculus is a bundle of counting rods and a counting board. The counting rods are usually made of bamboo sticks, about 12 cm- 15 cm in length, 2mm to 4 mm diameter, sometimes from animal bones, or ivory and jade (for well-heeled merchants). A counting board could be a table top, a wooden board with or without grid, on the floor or on sand. In 1971 Chinese archaeologists unearthed a bundle of well-preserved animal bone counting rods stored in a silk pouch from a tomb in Qian Yang county in Shanxi province, dated back to the first half of Han dynasty (206 BC – 8AD). In 1975 a bundle of bamboo counting rods was unearthed. The use of counting rods for rod calculus flourished in the Warring States, although no archaeological artefacts were found earlier than the Western Han Dynasty (the first half of Han dynasty; however, archaeologists did unearth software artefacts of rod calculus dated back to the Warring States); since the rod calculus software must have gone along with rod calculus hardware, there is no doubt that rod calculus was already flourishing during the Warring States more than 2,200 years ago. The key software required for rod calculus was a simple 45 phrase positional decimal multiplication table used in China since antiquity, called the nine-nine table, which were learned by heart by pupils, merchants, government officials and mathematicians alike. Rod numerals is the only numeric system that uses different placement combination of a single symbol to convey any number or fraction in the Decimal System.