Chinese abacus or suanpan

The suanpan (Simplified Chinese: 算盘; Traditional Chinese: 算盤; Pinyin: suànpán) of the Chinese dates from the Han Dynasty (202 BCE - 184 CE). Scanned and uploaded by Malcolm Farmer Source: Article for abacus, 9th edition Encyclopedia Britannica, volume 1 (1875) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Scanned and uploaded by Malcolm Farmer Source: Article for abacus, 9th edition Encyclopedia Britannica, volume 1 (1875) This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Simplified Chinese characters (Simplified Chinese: 简体字; Traditional Chinese: 簡體字; pinyin: jiÇŽntǐzì; also called 简化字/簡化字, jiÇŽnhuàzì) are one of two standard character sets of printed contemporary Chinese written language. ... Traditional Chinese characters are one of two standard character sets of printed contemporary Chinese written language. ... Pinyin (Simplified Chinese: 汉语拼音; Traditional Chinese: 漢語拼音; Pinyin: HànyÇ” PÄ«nyÄ«n), also known as scheme of the Chinese phonetic alphabet (Simplified Chinese: 汉语拼音方案; Traditional Chinese: 漢語拼音方案; Pinyin: HànyÇ” PÄ«nyÄ«n fāngàn), while pin means spell(ing) and yin means sound(s)), is a system of romanization (phonemic notation... The Han Dynasty (Traditional Chinese: 漢朝; Simplified Chinese: 汉朝; Hanyu Pinyin: ; Wade-Giles: Han Chau; 206 BC–AD 220) followed the Qin Dynasty and preceded the Three Kingdoms in China. ...

However, it rose to prominence during the Yuan Dynasty (1271 CE - 1368 CE). The Yuan Dynasty (Chinese: 元朝; pinyin: Yuáncháo; Mongolian: Dai Ön Yeke Mongghul Ulus) lasting officially from 1271 to 1368, occasionally known as the Mongol Dynasty. ...

The Chinese abacus is typically around 20 cm (8 inches) 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 each in the bottom 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 abacus 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. An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. ... Beech is a typical temperate zone hardwood The term hardwood designates wood from angiosperm trees. ...

Chinese abaci 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. In mathematics, multiplication is an arithmetic operation which is the inverse of division, and in elementary arithmetic, can be interpreted as repeated addition. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... 3 + 2 with apples, a popular choice in textbooks Addition is the basic operation of arithmetic. ... 5 - 2 = 3 Subtraction is one of the four basic arithmetic operations; it is essentially the opposite of addition. ... In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is For example, since This example suggests how square roots can arise when solving quadratic equations such as or... Plot of y = In mathematics, the cube root ( ) of a number is the number which, when cubed (multiplied by itself and then multiplied by itself again), gives back the original number. ...

See also: counting rods The counting rods (籌 chou2) were used by ancient Chinese before the invention of the abacus. ...

Origins

The earliest mention of an abacus in Chinese literature was in a 190 CE book of the Eastern Han Dynasty, namely Supplementary Notes on the Art of Figures written by Xu Yue in that year. However, the exact design of this abacus is not known. Events A part of Rome burns, and emperor Commodus orders the city to be rebuilt under the name Colonia Commodiana First year of Chuping era of Chinese Han Dynasty Births 190 is a number Deaths Athenagoras of Athens, Christian apologist Categories: 190 ... The Han Dynasty (Traditional Chinese: 漢朝; Simplified Chinese: 汉朝; Hanyu Pinyin: ; Wade-Giles: Han Chau; 206 BC–AD 220) followed the Qin Dynasty and preceded the Three Kingdoms in China. ...

In the famous long scroll Riverside Scenes at Qingming Festival painted by Zhang Zeduan at the latest during the Song Dynasty (960-1297), an abacus is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao). Zhang Zeduan (Traditional: 張擇端; Simplified: 张择端; pinyin: ; Wade-Giles: Chang Tse-tuan) was a Chinese painter. ... Zhang Zeduan (Traditional: 張擇端; Simplified: 张择端; pinyin: ; Wade-Giles: Chang Tse-tuan) was a Chinese painter. ... The Song Dynasty (Chinese: 宋朝) was a ruling dynasty in China from 960-1279. ... A historical re-enactor protraying a 19th century apothecary in Old Salem, North Carolina. ...

The similarity of the Roman abacus to the Chinese one suggests that the former could have inspired the latter. The Roman version apparently predates the Chinese one, and there is some evidence of a trade relationship between the classical world 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 (like most modern Japanese) has 4 plus 1 bead per decimal place, the standard Chinese abacus 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. Possibly the Roman abacus was used primarily for simple counting. The Romans developed the so-called fucken Roman abacus, or rather a portable counting board, based on previous Greek counting boards. ... james In mathematics and computer science, base-16, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ...

Another possible source of the Chinese abacus 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. Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus) to... 0 (zero) is both a number and a numeral. ... For the band, see Tang Dynasty (band). ... The decimal separator is used to mark the boundary between the integer and the fractional parts of a decimal numeral. ...

Beads

There are two types of beads on the abacus, 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, and carry a value of 1 in their column. The ones in the upper deck are sometimes called heaven beads. The columns are much like the places in Arabic numerals: one of the columns, usually the rightmost, represents the ones place; to the left 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 Chinese abacus, 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, Quichu, 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 Chinese abacus multiplication and division).

The mnemonics/readings of the Chinese division method [Quichu] has its origin in the use bamboo sticks [Chousuan], which is one of the reasons that many believe the evolution of Chinese Abacus [Sunpan] 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 1920's.

The beads and rods are often lubricated to ensure quick, smooth motion.

Decimal system

This device works as a bi-quinary based number system in which carries and shiftings are similar to the decimal number system. Since each rod represents a digit in a decimal number, the computation capacity of the abacus is only limited by the number of rods on the abacus. When a mathematician runs out of rods, another abacus can be added to the left of the first. In theory, the abacus can be expanded indefinitely in this way. Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, including the Colossus. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ...

Hexadecimal system

Traditional Chinese weighing units was a hexadecimal system. One jin (斤) equals sixteen liang (兩). Abaci were commonly used in market place to calculate with these hexadecimal units. When all the beads in the Chinese abacus are used, each column can be used to represent numbers between 0 to 15 (two 5s and five 1s.) Computation in decimal and hexadecimal is very similar except one extra bead from both the upper and lower deck are used. james In mathematics and computer science, base-16, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ...

Modern decline in use

Abacus 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 handheld calculators became readily available, schoolchildren's willingness to learn the use of the abacus decreased dramatically. In the early days of handheld calculators, news of abacus 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 abaci can be built to virtually limitless precision. But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the abacus could never compute higher functions – such as those in trigonometry – faster than a calculator. Nowadays, as calculators have become more affordable, abaci are not commonly used in Hong Kong or Taiwan, but many parents still send their children to private tutors or school- and government- sponsored afterschool 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. Abaci are still being used elsewhere in China and in Japan. Motto: None Anthem: National Anthem of the ROC Capital Taipei City (de facto) Nanjing (de jure) 1 Largest city Taipei City Official language(s) Mandarin (Guoyü) Government • President • Vice President • Premier Multiparty democracy Chen Shui-bian Annette Lu Su Tseng-chang Establishment • Xinhai Revolution Declared  October 10, 1911 Established  January... A modern basic arithmetic calculator For other uses, see Calculator (disambiguation). ... Wikibooks has more about this subject: Trigonometry Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent. ... Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. ...

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.

Miscellanea

The suanpan is closely tied to the Chinese "huāmǎ" numbering system. Due to technical limitations, some web browsers may not display some special characters in this article. ...

Modern versions of the suanpan may have a button connected to a pair of rods, pushing all the beads back to the zero position.

External links

• Chinese Abacus Tutor - See the steps in addition and subtraction
• A Traditional Suan Pan Technique for Multiplication