AbacuS

#REDIRECT Abacus

Abacus

An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It was in use centuries before the adoption of the written Arabic numerals system and is still widely used by merchants and clerks in China and elsewhere. == Chinese abacus == The suanpan () of the China is similar to the Roman abacus in principle, though has a different construction. 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 hard wood. 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. 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 (mathematics), addition, subtraction, square root and cube root operations at high speed. Bead arithmetic is the calculating technique used with various types of abaci, in particular the Chinese abacus. See Chinese abacus for more information. == Roman abacus == The Roman Empire Roman abacus shown here in reconstruction contains seven long and seven shorter grooves, the former having up to five beads in each and the latter one. The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives—five units, five tens, ''etc.'', essentially in a bi-quinary coded decimal system, obviously related to the Roman numerals. The short grooves on the right may have been used for marking Roman ounces. Computations are made by means of beads which would probably have been slid up and down the grooves to indicate the value of each column.
See Roman abacus for more information. == Japanese abacus == The Japanese eliminated (first) one bead from the upper deck and (later) another bead from lower deck in each column of the Chinese abacus, the Japanese eliminated the use of Quichu (Chinese division table). The method of Chinese division table were still used when there were 5 lower beads. There came the war of Multiplication table versus Division Table. The school of Multiplication table prevailed in 1920s. The rods (number of digits) increase to usually 21, 23, 27 or even 31, thus allow calculation for more digits. That "modernization" makes the Japanese soroban (算盤) (apparently) more compliant to the decimal system than the Chinese Abacus. Soroban is taught in elementary schools as a part of lessons in mathematics. When teaching the soroban, a song-like instruction is given by the tutor. The soroban is about 8 cm (3 inches) tall. The beads on a soroban are usually shaped as a double cone (bi-cone) to facilitate ease of movement. Ironically, the primary students bring along with them two soroban, one of 1 upper bead and 5 lower beads, the other of 1 upper bead with 4 lower beads, when they learn soroban in school! The size of beads of soroban is standardized, the Japanese classified soroban for native Japanese and foreigners, as Western people are of bigger body build and hands/fingers. The soroban that are for foreigners (Westerners) are made with plastic pipe on on both left and right side of the frame, while that that for native Japanese were all made with all wooden frame. In this way the "thickness" of the soroban (for foreigners) is higher, render it easier for the non-Japanese to manipulate. http://www.syuzan.net/english/history/history.html https://www.soroban.com/deal_eng.html https://www.soroban.com/d3.html == Russian abacus == The Russian abacus, the schoty or sjotty (счёты), usually has a single slanted deck, with ten beads on each wire (except one wire which has four, and acts as a separator or for fractions). This wire is usually near the user. The Russian abacus is often used vertically, with wires from left to right in the manner of a book. The wires are usually bowed to bulge upward in the center, in order to keep the beads pinned to either of the two sides. It is cleared when all the beads are moved to the right. During manipulation, beads are moved to the left. For easy viewing, the middle 2 beads on each wire (the 5th and 6th bead) usually have a colour different to the other 8 beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color. The Russian abacus is still in common use today in shops and markets throughout the Commonwealth of Independent States, although it is no longer taught in most schools. == Native American abacus == Some sources also mention the use of the abacus in ancient Mayan culture. The Mesoamerican abacus uses the 5-digit base-20 Mayan numerals system. The khipu of the Inkas was a system of knotted cords used to record numerical data - like advanced tally sticks - but was not used to perform calculations. == School abacus == Around the World, abaci have been used in elementary schools as an aid in teaching arithmetics. In Western countries, a model similar to the Russian abacus and often known as a bead frame has been common (see image). == Computers == A computer is an automaton digital circuit abacus. Some history of computing used ten switching elements per numeral, but a modern computer is a binary number system abacus. == Uses by the visually impaired == Abaci are still used by individuals who have blindness. They use an abacus to perform the mathematical functions multiplication, division (mathematics), addition, subtraction, square root and cubic root. A piece of soft fabric is placed behind the beads so that they don't move inadvertently. This keeps the beads in place while a person feels the beads or uses the abacus. == See also == * Slide rule * Napier's bones * History of computing * History of computing hardware * Nepohualtzintzin (Native American abacus - Aztec) * Abacus logic * Abacus system * Positional notation ==External links== * [http://www.cut-the-knot.org/blue/Abacus.shtml Abacus in Various Number Systems] * [http://www.cut-the-knot.org/Curriculum/Arithmetic/Soroban.shtml Soroban in Various Number Systems] * [http://www.cut-the-knot.org/Curriculum/Arithmetic/SuanPan.shtml Suan pan in Various Number Systems] * [http://encyclopedia.jrank.org/A10_ADA/ABACUS_Gr_15t_34_a_slab_Fr_aba.html Abacus] Article about abacus from the 11th edition Encyclopedia Britannica (1911). * [http://www.ee.ryerson.ca/~elf/abacus/ Abacus] * [http://webhome.idirect.com/~totton/abacus/ Abacus: Mystery of the Bead] - An Abacus Manual * [http://webhome.idirect.com/~totton/soroban/ Advanced Abacus Techniques] * [http://webhome.idirect.com/~totton/abacus/Lee/ Lee Kai-chen's Improved Abacus] * [http://www.soroban.com/ Soroban] * [http://www.gis.net/~daveber/Abacus/Abacus.htm Soroban Abacus Handbook] A guide to addition, subtraction, multiplication and division. * [http://www.sungwh.freeserve.co.uk/sapienti/abacus01.htm Suan Pan] * Webarchive backup: [http://web.archive.org/web/20011202050525/hawk.hama-med.ac.jp/dbk/abacus.html Mesoamerican abacus] (this site is no longer online - but the webarchive backup is; however, one of the author’s documents comparing the organization and use of the Mesoamerican abacus and the Chinese abacus is mirrored at [http://www.ee.ryerson.ca/~elf/abacus/dbk/]); see also [http://www.peterassociates.com/mayan-abacus.htm] * [http://www.dotpoint.com/xnumber/pic_roman_abacus.htm Roman abacus] * [http://www.abacus.ca/abacus-images.php Abacus Photos and Images] * [http://www.research.ibm.com/atomic/nano/roomtemp.html The World’s Smallest Abacus] * [http://www.tux.org/~bagleyd/abacus.html Java applet of Chinese, Japanese and Russian abaci] fa:چرتکه nah:Nepohualtzintzin Ancient Rome Computation Mathematical tools Mechanical calculators

Abacus

This text came from an old public domain resource (copyright now expired) and, it turns out, duplicated an entry already added under an OldLink; I've redirected that page to this one. I wonder, though, if we should preserve the text as-is, as was done on the old one, or make every attempt to update it so it's useful as something other than a sociological curiosity. I personally favor updating it, but it won't be a problem to restore the old text in its original form if that's what the consensus is. --KQ ---- Yes! Yes! Update, combine, rearrange, add. :Be bold in updating pages! I also OK to mention Britannica and Gutenberg by reference on Talk pages, just don't mention either of them on the page itself, or credit them just to give credit. --User:Lee Daniel Crocker ---- While the page mentions the structure of various abaci and says they can be use for addition through cubic roots(!) I would very much like to see a description of how they can be used as such. Any experts out there care to add? == Category:Computer science == Does this really belong in that category? User:Siroxo 18:46, Jun 23, 2004 (UTC) == Nepohualtzintzin == I clicked on the link to this at the bottom of the article, half expecting to see a wonderful write-up about Aztec scientific technology. Instead, it redirects back to this page. Abacus -> Nepohualtzintzin -> Abacus...not encouraging. --User:Ardonik 04:18, Jul 10, 2004 (UTC) == tie to Roman Abacus??? == :Its similarity to the Roman abacus suggests that that was the ultimate source, and this was very possible, since there were direct trade relations between the classical world and China, and Mongol traders along the Silk Road were a bridge between East and West. It could even have been introduced by the Roman legion captured by the Persians and sold to the Chinese emperor as engineers. Most were later ransomed, but many found China much to their liking. This connection is way too far-fetched in my opinion for several reasons: *There are more dissimilarities than similarities. *Roman uses removable beads *Chinese uses sliding beads *Roman abacus uses 1-plus-4 beads to represent decimal numbers *Chinese abacus uses 2-plus-5 beads to represent either decimal or hexadecimal numbers *Roman used the abacus purely as a counting tool. *Chinese used it as a calculating device by developing advanced computation techniques to do multiplication, divison, square root and cubic root on the abacus. Such claim needs more evidence than just pure speculations. User:Kowloonese 01:14, 2 Sep 2004 (UTC) :: This is not pure speculation. Claiming the Mayans were influenced by the Egyptians solely because of a similarity of large buildings that exist in both civilization is an example of ''PURE'' speculation. There was no opportunity for the two cultures to come into contact. ::The Roman abacus dates back to at least 100 BCE. ::The well-known version of the Chinese abacus, the Suan Pan, emerged in the 13th century, when most of the cultures in the world were using the 10-digit positional notation system which, almost one thousand years earlier, the Romans lacked. ::The Yuan Dynasty (1271-1368) was when the Mongols rule China. It was a period of cultural enlightenment. The Mongols replaced the Han Chinese bureaucrats and all important central and regional posts within China were monopolized by Mongols, who also preferred employing non-Chinese from other parts of the Mongol domain--Central Asia, the Middle East, and even Europe to fill positions for which no Mongol could be found. Scientic education, literacy, and public works florished under Mongols. It was in this melting pot of cultures and enlightenment, that the Suan Pan leaped into existance as a fully formed two-deck abacus in the 13th century. ::Admittedly, as far back at 190 CE, there were references to abaci in China. It was mentioned in a book of the Eastern Han Dynasty, namely ''Supplementary Notes on the Art of Figures'' written by Xu Yue in that year. Of course, this was at the height of the Roman Empire. In addition to trading via the Mongols along the Silk Road, there is proof of direct contact between the cultures. ''Hou Hanshu'' (History of the Later Han) recounts that a Roman convoy set out by emperor Antoninus Pius reached the Chinese capital Luoyang in 166 CE and was greeted by Emperor Huan. ::Chinese Trade in the Tang Dynasty (618-907) along the Indian Ocean and the Middle East would have provided direct contact with India and Islam allowing them to accquire the concept of Zero and the decimal point from Indian and Islamic merchants and mathematicians. ::Another reference to an abacus in China occurred at the latest during the Song Dynasty (960-1297), when Zhang Zeduan painted his Riverside Scenes at Qingming Festival. In this famous long scroll, an abacus is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao). Worthy of note is the increased Mongol influences as Song Dynasty collapsed under Mongol incursions. ::By the 13th century, the Chinese numeral system is a fully expressed 10-digit system with positional notation, so it is not unreasonable to expect the Chinese to have developed computing techniques for the abacus that are readily expressed as algorisms under a positional notation system. ::Any form of advanced arithmetic is extremely difficult using Roman numerals which lacked the Zero and positional notation. Before an arithmetic operation could be transfered to an abacus, someone had to develop the algorism for the operation. The complexity of multiplication and division under Roman arithmetic did not mean they were limited to only counting on an abacus. The limitation of the advanced arithmetic operations is a function of limitations of the Roman numeral system and not their abaci. ::The adaption of the Roman abacus to the needs of the Chinese numeral system could be the cause of the mutation from 1/4 to 2/5 beads. I have found no evidence for or against early Chinese abaci having other than the 2/5 configuration. If a Roman abacus was presented to the Han Emperor in 166 CE, (no doubt the staff and merchants whom accompanied the envoy would have had abaci as well) then the intervening centuries were sufficently long enough for the Chinese to make the abacus their 'own' by adapting to their needs. ::Furthermore, I did find an obscure reference that there was a Roman abacus with 2/5 configuration, but I am not sure if the author was correct. The author of the article cites K. Menninger, Number Words and Number Symbols (New York: Dover, 1992) as the source. ::Note that the text of the article did not assert the connection was proven. However, I believe that there is more than enough evidence to ''suggest'' such a connection and that such a connection is not pure speculation as you claim. If more evidence presents itself, I am sure references will be cited and proofs offered. :::--User:Denorris 05:18, Sep 2, 2004 (UTC) :::: Updated--User:Denorris 12:20, Sep 2, 2004 (UTC) ::::: Updated--User:Denorris 13:39, Sep 2, 2004 (UTC) :::I am not convinced despite everything you quoted here. There were many similar inventions in Chinese and Western culture that were proven to be developed independently. Almost all cultures around the world figured out what a year and a month is because they all looked at the same sky, not because they made contact and shared notes. Almost all cultures around the world figured out how to count in ten. Not because the cultures had contact with each other, it was because human beings have the common physiology, the ten fingers. The 1/4 bead counting came naturally when people used one hand to count while the other hand was busy sorting things. People count in ten because of ten fingers in two hands, people modified it into 1/4 counting because one hand got busy and then they figured out that they can count using the thumb to represent 5 and the fingers to represents ones. The abacus could very well be a natural extention to finger counting. Chinese and Roman could easily come up with the same idea independently. :::You could believe Mayan and Egyptian could came up with large buildings independently because you couldn't find any evidence that the two cultures made contact. What if the evidence show up tomorrow, will you then claim Mayan and Egyptian learned their building technique from each others? Substitute buildings with abaci, then the same argument becomes very weak. Proving Chinese and Roman had contact does not prove their abaci are related. :::In my opinion, the 1/4 and 2/5 design of the abaci were developed independently. And Chinese stuck with the same design all along because they used it for both decimal and hexadecimal calculation. The Japanese adopted the Chinese abacus, but they didn't use them for hexadecimal calculation, and they removed the two redundent beads and resulted to a design very similar to the Roman abacus. :::Another example is the weighing unit in China and the Imperial weighing unit from England. Chinese had one jin for 16 liang while the English had one pound for 16 ounces. You can argue they learned from each other because they made contact and the hexadecimal approaches are strikingly similar. However, when you understand the 16 based unit were natural result from using a beam balance scale to make division. For example, you spit one pound of your grains into two piles until the scale balances on both size, you repeat it 4 times and you get an ounce. The Chinese did the same with their grain to come up with the similar 16 base units. Whether the two cultures made contact or not is irrelevant. :::Unless you have found literature that explained the origin of the abaci, the claim in the article is baseless and should be removed. User:Kowloonese 07:59, 3 Sep 2004 (UTC) ::::Perhaps the problem here lies with understanding the what is meant by the word 'suggests'? ::::In the context used here, I define suggests as 'To bring or call to mind by logic or association'. ::::I don't see where I set out to convince anyone that they are related. The fact is that we just don't know and may never know, but the circumstantial evidence that ''suggests'' they could be related. ::::--User:Denorris 08:41, Sep 3, 2004 (UTC) :::::No, I think the problem here lies in whether certain suggestions are likely or not. If the possibility is there but remote, it is not worth putting in an encylopedia article. I "suggest" the opposite. I "suggest" that the similarity is due to the fact that both Chinese and Roman have 5 fingers in each hand, not because Roman contacted Chinese back in 166 CE. It is also possible that some alien civilization invented the abaci, but I rather not make such kind of suggestion here. User:Kowloonese 18:39, 3 Sep 2004 (UTC) ::::::I think you have a great idea. Why not suggest your alternative speculation in the article as well? We can make a subsection called 'Origins' and suggest both possibilties, present the underlaying evidence and allow the reader to decide what is non-trival content or not. We can refer the reader to the this entry in the discussion section for further infomation as well. ::::::While we are at it, perhaps the article should be moved to its own page and a stub left here? We can also move this discussion to the new page. :::::::--User:Denorris 20:36, Sep 3, 2004 (UTC) ::::::::So you believe in alien? I don't think I can find any supporting evidence. :-) I think the debate does not belong to the article. This talk page serves the purpose. User:Kowloonese 21:38, 3 Sep 2004 (UTC) :::::::::So our discussion is at an end as I have nothing left to debate. If you wish to continue debating this, I will have to ask that it be done under the confines of Wikipedia:Requests for mediation as I believe I have tried to offer reasonable solution. Feel free to make a such a request and flag the article NPOV until such time as this is resolved. ::::::::::--User:Denorris 22:11, Sep 3, 2004 (UTC) :::::::::::Agree. End of discussion. I added a few sentences to the article too. I guess you knew the alien part was just a joke. User:Kowloonese 22:50, 3 Sep 2004 (UTC) ::::::::::::Good enough. I believe that the Chinese abacus section is long enough to justify is own page and unless you strongly object, I will spin it off, leaving a stub here. I will also clarify the origins debate, additionally moving and referencing the bulk of our revelent discussion to the new page's Talk section. ::::::::::::Yes, the ':-)' gave away the fact that you was joking and not making an ad hominem attack, tho I did check with my controllers on Tau Ceti just to make sure! ;-) :::::::::::::--User:Denorris 23:07, Sep 3, 2004 (UTC) ::::::::::::::No one owns any article in wikipedia. You don't need my agreement before you do the spin off. Go ahead. User:Kowloonese 23:19, 3 Sep 2004 (UTC) == Suggest 3 possible wiki links for Abacus. == An User:Nickj/Link_Suggester has some possible wiki link suggestions for the Abacus article: * Can link upper deck: ...re 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 hexa... (Abacus#Chinese abacus) * Can link decimal system: ...nese abacus, because these beads are redundant when used in Decimal. That makes the Japanese soroban (算盤) m... (Abacus#Japanese abacus) * Can link mathematical functions: ... visual impairments. They use an abacus to perform the Function (mathematics) multiplication, division, addition, [[subtracti... (Abacus#Uses by the visually impaired) ''Notes'': The article text has not been changed in any way; Some of these suggestions may be wrong, some may be right.
''User talk:LinkBot'': User:Nickj/Link Suggester/Positive Feedback, User:Nickj/Link Suggester/Negative Feedback, User:Nickj/Link Suggester/Don't link to — User:LinkBot 11:30, 1 Dec 2004 (UTC) == Abacus use in Russia == I live in Novosibirsk and I did not see an abacus in use for a long time neither here nor in Berdsk (a small town nearby) despite what the "Russian abacus" section currently says. Can anyone confirm if abacus is still used somewhere in Russia? --User:Mivlad 00:45, 19 Jun 2005 (UTC) :I believe that I'm the one who added that bit to the article. I lived in Karaganda, Kazakhstan for a year (in 2002) and saw the russian abacus used by the sellers every day at my local markets. Not used by everybody, but still quite common, in several different locations. Karaganda being the third most developed city in the country, I suspect that the abacus is even more prevalent in the rural areas of Kazakhstan and Russia, not to mention the other (lesser developed) republics. --User:Staecker 05:15, 19 Jun 2005 (UTC) ::May I suggest we replace :::''The Russian abacus is still in common use today in shops and markets throughout the Commonwealth of Independent States, although it is no longer taught in most schools.'' ::by :::''The Russian abacus is still in use today in shops and markets throughout the Commonwealth of Independent States, although it is being replaced by other means of calculation and is no longer taught in most schools.'' --User:Noe 20:33, Jun 21, 2005 (UTC) ::: That sounds very good. In fact, I heard from some folks (don't really know if it's true) that the government was beginning to require that people use digital calculators or cash registers, and that the abacus holdouts were technically breaking the rules. --User:Staecker 21:02, 21 Jun 2005 (UTC)

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AbacuS
Abacus
Abacus
Abacus_(architecture)
Abacus_(Aztec)
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Abacus_system