The suanpan (simplified Chinese: 算盘; traditional Chinese: 算盤; pinyin: suànpán), also spelled suan pan or souanpan) is an abacus of Chinese origin. The earliest known written documentation of the Chinese abacus dates to the 2nd century BCE during the Han dynasty, and it was later described in a 190 CE book of the Eastern Han dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue. However, the exact design of this suanpan is not known. Usually, a suanpan is about 20 cm (8 in) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads on each rod in the bottom deck. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam. The suanpan can be reset to the starting position instantly by a quick jerk around the horizontal axis to spin all the beads away from the horizontal beam at the center. Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient suanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed. The modern suanpan has 4+1 beads, colored beads to indicate position and a clear-all button. When the clear-all button is pressed, two mechanical levers push the top row beads to the top position and the bottom row beads to the bottom position, thus clearing all numbers to zero. This replaces clearing the beads by hand, or quickly rotating the suanpan around its horizontal center line to clear the beads by centrifugal force.
History
The word "abacus" was first mentioned by Xu Yue (160–220) in his book suanshu jiyi (算数记遗), or Notes on Traditions of Arithmetic Methods, in the Han dynasty. As it described, the original abacus had five beads (suan zhu) bunched by a stick in each column, separated by a transverse rod, and arrayed in a wooden rectangle box. One in the upper part represents five and each of four in the lower part represents one. People move the beads to do the calculation. The long scroll Along the River During Qing Ming Festival painted by Zhang Zeduan (1085–1145) during the Song dynasty (960–1279) might contain a suanpan beside an account book and doctor's prescriptions on the counter of an apothecary. However, the identification of the object as an abacus is a matter of some debate. Zhusuan was an abacus invented in China at the end of the 2nd century CE and reached its peak during the period from the 13th to the 16th century CE. In the 13th century, Guo Shoujing (郭守敬) used Zhusuan to calculate the length of each orbital year and found it to be 365.2425 days. In the 16th century, Zhu Zaiyu (朱載堉) calculated the musical Twelve-interval Equal Temperament using Zhusuan. And again in the 16th century, Wang Wensu (王文素) and Cheng Dawei (程大位) wrote respectively Principles of Algorithms and General Rules of Calculation, summarizing and refining the mathematical algorithms of Zhusuan, thus further boosting the popularity and promotion of Zhusuan. At the end of the 16th century, Zhusuan was introduced to neighboring countries and regions. A 5+1 suanpan appeared in the Ming dynasty, an illustration in a 1573 book on suanpan showed a suanpan with one bead on top and five beads at the bottom. The evident similarity of the Roman abacus to the Chinese one suggests that one may have inspired the other, as there is strong evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci could be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model and Chinese model (like most modern Japanese) has 4 plus 1 bead per decimal place, the old version of the Chinese suanpan has 5 plus 2, allowing less challenging arithmetic algorithms. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model run in grooves, presumably more reliable since the wires could be bent. Another possible source of the suanpan is Chinese counting rods, which operated with a place value decimal system with empty spot as zero. Although sinologist Nathan Sivin claimed that the abacus, with its limited flexibility, "was useless for the most advanced algebra", and suggested that "the convenience of the abacus" may have paradoxically stymied mathematical innovation from the 14th to 17th centuries, Roger Hart counters that the abacus in fact facilitated new developments during that time, such as Zhu Zaiyu's treatises on musical equal temperament, for which he used nine abacuses to calculate √200 to twenty-five digits.
Beads There are two types of beads on the suanpan, those in the lower deck, below the separator beam, and those in the upper deck above it. The ones in the lower deck are sometimes called earth beads or water beads, and carry a value of 1 in their column. The ones in the upper deck are sometimes called heaven beads and carry a value of 5 in their column. The columns are much like the places in Indian numerals: one of the columns, usually the rightmost, represents the ones place; to the left of it are the tens, hundreds, thousands place, and so on, and if there are any columns to the right of it, they are the tenths place, hundredths place, and so on.
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