Suanpan
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The suanpan (simplified Chinese: 算盘; traditional Chinese: 算盤; pinyin: suànpán) is an abacus of Chinese origin first 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.[1] The suanpan rose to prominence during the Yuan Dynasty (1271 CE - 1368 CE).
Usually, a suanpan is about 20 cm tall and it comes in various widths depending on the application. It usually has more than seven rods. There is one bead on each rod in the upper deck and four beads on each rod in the bottom deck. This configuration is used for both decimal and hexadecimal computation. 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 along 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.
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[edit] History
In the famous long scroll Riverside Scenes at Qingming Festival painted by Zhang Zeduan (1085-1145) during the Song Dynasty (960-1297), a suanpan is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao).
The similarity of the Roman abacus to the Chinese one suggests that one could have inspired the other, as there is some evidence of a trade relationship between the Roman Empire and China. However, no direct connection can be demonstrated, and the similarity of the abaci may 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, and also allowing use with a hexadecimal numeral system. Instead of running on wires as in the Chinese and Japanese models, the beads of Roman model runs in groves, presumably making arithmetic calculations much slower.
Another possible source of the suanpan is Chinese counting rods, which operated with a decimal system but lacked the concept of a zero as a place holder. The zero was probably introduced to the Chinese in the Tang Dynasty (618-907) when travel in the Indian Ocean and the Middle East would have provided direct contact with India and Islam allowing them to acquire the concept of zero and the decimal point from Indian and Islamic merchants and mathematicians.
[edit] 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 Arabic 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.
At the end of a decimal calculation on a suanpan, it is never the case that all five beads in the lower deck are moved up; in this case, the five beads are pushed back down and one carry bead in the top deck takes their place. Similarly, if two beads in the top deck are pushed down, they are pushed back up, and one carry bead in the lower deck of the next column to the left is moved up. In hexadecimal calculation, all seven beads on each column are used. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck.
The earth beads and heaven beads are usually not used in addition and subtraction. They are essential (compulsory) in some of the multiplication methods [2 amongst 3 methods requires them] and Division method [special division table, Qiuchu 九歸 , 1 amongst 3 methods]. When the intermediate result (in multiplication and division) is larger than 15 (fifteen), the lower of the upper bead is moved halfway to represent ten [xuanchu, suspended]. Thus the same rod can represent up to 19 (compulsory as intermediate steps in tradition suanpan multiplication and division).
The mnemonics/readings of the Chinese division method [Qiuchu] has its origin in the use bamboo sticks [Chousuan], which is one of the reasons that many believe the evolution of suanpan is independent of the Roman Abacus.
This Chinese division method [i.e. with division table] was not in use when the Japanese changed their abacus to 1 upper bead and 4 lower beads in about the 1920's.
The beads and rods are often lubricated to ensure quick, smooth motion.
[edit] Decimal system
This device works as a bi-quinary based number system in which carries and shifting are similar to the decimal number system. Since each rod represents a digit in a decimal number, the computation capacity of the suanpan is only limited by the number of rods on the suanpan. When a mathematician runs out of rods, another suanpan can be added to the left of the first. In theory, the suanpan can be expanded indefinitely in this way.
[edit] Hexadecimal system
Traditional Chinese weighing units was a hexadecimal system. One jin (斤) equals sixteen liang (兩). Suanpans were commonly used in market place to calculate with these hexadecimal units. When all the beads in the suanpan are used, each column can be used to represent numbers between 0 to 9 (one 5 and four 1s.) Computation in decimal and hexadecimal is very similar except one extra bead from both the upper and lower deck are used.
[edit] Decline in modern usage
Suanpan arithmetic was still being taught in school in Hong Kong as recently as the late 1960s, and in Republic of China into the 1990s. However, when hand held calculators became readily available, school children's willingness to learn the use of the suanpan decreased dramatically. In the early days of hand held calculators, news of suanpan operators beating electronic calculators in arithmetic competitions in both speed and accuracy often appeared in the media. Early electronic calculators could only handle 8 to 10 significant digits, whereas suanpans can be built to virtually limitless precision. But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the suanpan could never compute higher functions – such as those in trigonometry – faster than a calculator. Nowadays, as calculators have become more affordable, suanpans are not commonly used in Hong Kong or Taiwan, but many parents still send their children to private tutors or school- and government- sponsored after school activities to learn bead arithmetic as a learning aid and a stepping stone to faster and more accurate mental arithmetic, or as a matter of cultural preservation. Speed competitions are still held. Suanpans are still being used elsewhere in China and in Japan, as well as in some few places in Canada and the United States.
In mainland China, formerly accountants and financial personnel had to pass certain graded examinations in bead arithmetic before they were qualified. Starting from about 2003 or 2004, this requirement has been entirely replaced by computer accounting.
[edit] Miscellanea
The suanpan is closely tied to the Chinese "huāmǎ" numbering system.
Modern versions of the suanpan may have a button connected to a pair of rods, pushing all the beads back to the zero position.
[edit] Notes
- ^ Peng Yoke Ho, page 71
[edit] References
- Peng Yoke Ho (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Courier Dover Publications. ISBN ISBN 0486414450.
[edit] See also
[edit] External links
- Suanpan Tutor - See the steps in addition and subtraction
- A Traditional Suan Pan Technique for Multiplication
