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The abacus (pluralabaci or abacuses), also called a counting frame, is a calculating tool that was in use in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the written Hindu–Arabic numeral system.^[1] The exact origin of the abacus is still unknown. Today, abacuses are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves of sand or on tablets of wood, stone, or metal.

Abacuses come in different designs. Some designs, like the bead frame consisting of beads divided into tens, are used mainly to teach arithmetic, although they remain popular in the post-Soviet states as a tool. Other designs, such as the Japanese soroban, have been used for practical calculations even involving several digits. For any particular abacus design, there are usually numerous different methods to perform a certain type of calculation, which may include basic operations like addition and multiplication, or even more complex ones, such as calculating square roots. Some of these methods may work with non-natural numbers (numbers such as 1.5 and ​³⁄₄).

Although today many use calculators and computers instead of abacuses to calculate, abacuses still remain in common use in some countries. Merchants, traders and clerks in some parts of Eastern Europe, Russia, China and Africa use abacuses, and they are still used to teach arithmetic to children.^[1] Some people who are unable to use a calculator because of visual impairment may use an abacus.

• 2History
• 13External links

Etymology[edit]

The use of the word abacus dates before 1387 AD, when a Middle English work borrowed the word from Latin to describe a sandboard abacus. The Latin word came from Greekἄβαξabax which means something without base, and improperly, any piece of rectangular board or plank.^[2][3][4] Alternatively, without reference to ancient texts on etymology, it has been suggested that it means 'a square tablet strewn with dust',^[5] or 'drawing-board covered with dust (for the use of mathematics)'^[6] (the exact shape of the Latin perhaps reflects the genitive form of the Greek word, ἄβακoςabakos). Whereas the table strewn with dust definition is popular, there are those that do not place credence in this at all and in fact state that it is not proven.^{[7][nb 1]} Greek ἄβαξ itself is probably a borrowing of a Northwest Semitic, perhaps Phoenician, word akin to Hebrewʾābāq (אבק), 'dust' (or in post-Biblical sense meaning 'sand used as a writing surface').^[8]

The preferred plural of abacus is a subject of disagreement, with both abacuses^[9] and abaci^[9] (hard 'c') in use. The user of an abacus is called an abacist.^[10]

History[edit]

Mesopotamian[edit]

The period 2700–2300 BC saw the first appearance of the Sumerian abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.^[11]

Some scholars point to a character from the Babyloniancuneiform which may have been derived from a representation of the abacus.^[12] It is the belief of Old Babylonian^[13] scholars such as Carruccio that Old Babylonians 'may have used the abacus for the operations of addition and subtraction; however, this primitive device proved difficult to use for more complex calculations'.^[14]

Egyptian[edit]

The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the Egyptians manipulated the pebbles from right to left, opposite in direction to the Greek left-to-right method. Archaeologists have found ancient disks of various sizes that are thought to have been used as counters. However, wall depictions of this instrument have not been discovered.^[15]

Persian[edit]

During the Achaemenid Empire, around 600 BC the Persians first began to use the abacus.^[16] Under the Parthian, Sassanian and Iranian empires, scholars concentrated on exchanging knowledge and inventions with the countries around them – India, China, and the Roman Empire, when it is thought to have been exported to other countries.

Greek[edit]

The earliest archaeological evidence for the use of the Greek abacus dates to the 5th century BC.^[17] Also Demosthenes (384 BC–322 BC) talked of the need to use pebbles for calculations too difficult for your head.^[18][19] A play by Alexis from the 4th century BC mentions an abacus and pebbles for accounting, and both Diogenes and Polybius mention men that sometimes stood for more and sometimes for less, like the pebbles on an abacus.^[19] The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome and, until the French Revolution, the Western Christian world.

A tablet found on the Greek island Salamis in 1846 AD (the Salamis Tablet), dates back to 300 BC, making it the oldest counting board discovered so far. It is a slab of white marble 149 cm (59 in) long, 75 cm (30 in) wide, and 4.5 cm (2 in) thick, on which are 5 groups of markings. In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line. Below these lines is a wide space with a horizontal crack dividing it. Below this crack is another group of eleven parallel lines, again divided into two sections by a line perpendicular to them, but with the semicircle at the top of the intersection; the third, sixth and ninth of these lines are marked with a cross where they intersect with the vertical line.^[20] Also from this time frame the Darius Vase was unearthed in 1851. It was covered with pictures including a 'treasurer' holding a wax tablet in one hand while manipulating counters on a table with the other.^[18]

Chinese[edit]

The earliest known written documentation of the Chinese abacus dates to the 2nd century BC.^[21]

The Chinese abacus, known as the suanpan (算盤, lit. 'calculating tray'), is typically 20 cm (8 in) tall and comes in various widths depending on the operator. 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. The beads are usually rounded and made of a hardwood. The beads are counted by moving them up or down towards the beam; beads moved toward the beam are counted, while those moved away from it are not.^[22] The suanpan can be reset to the starting position instantly by a quick movement along the horizontal axis to spin all the beads away from the horizontal beam at the center.

The prototype of the Chinese abacus appeared during the Han Dynasty, and the beads are oval. The Song Dynasty and earlier used the 1:4 type or four-beads abacus similar to the modern abacus commonly known as Japanese-style abacus.^{[citation needed]}

In the early Ming Dynasty, the abacus began to appear in the form of 1:5 abacus. The upper deck had one bead and the bottom had five beads.^{[citation needed]}

In the late Ming Dynasty, the abacus styles appeared in the form of 2:5.^{[citation needed]} The upper deck had two beads, and the bottom had five beads. It can express hexadecimal or smaller bases, because the calculation method at that time included the Chinese catty equal to sixteen tael（一斤十六兩）.^{[citation needed]}

Various calculation techniques were devised for Suanpan enabling efficient calculations. There are currently schools teaching students how to use it.

In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible 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 abacuses may be coincidental, both ultimately arising from counting with five fingers per hand. Where the Roman model (like most modern Korean and Japanese) has 4 plus 1 bead per decimal place, the standard suanpan has 5 plus 2. (Incidentally, this allows use with a hexadecimal numeral system, which was used for traditional Chinese measures of weight.) Instead of running on wires as in the Chinese, Korean, and Japanese models, the beads of Roman model run in grooves, 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 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, allowing them to acquire the concept of zero and the decimal point from Indian merchants and mathematicians.

Roman[edit]

The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe, and persisted in limited use into the nineteenth century.^[23] Due to Pope Sylvester II's reintroduction of the abacus with modifications, it became widely used in Europe once again during the 11th century^[24][25] This abacus used beads on wires, unlike the traditional Roman counting boards, which meant the abacus could be used much faster.^[26]

Writing in the 1st century BC, Horace refers to the wax abacus, a board covered with a thin layer of black wax on which columns and figures were inscribed using a stylus.^[27]

One example of archaeological evidence of the Roman abacus, shown here in reconstruction, dates to the 1st century AD. It has eight long grooves containing up to five beads in each and eight shorter grooves having either one or no beads in each. 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, related to the Roman numerals. The short grooves on the right may have been used for marking Roman 'ounces' (i.e. fractions).

Indian[edit]

The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that 'placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one, while placing the wick on the number hundred means it is called a hundred, and on the number one thousand means it is a thousand'. It is unclear exactly what this arrangement may have been. Around the 5th century, Indian clerks were already finding new ways of recording the contents of the Abacus.^[28] Hindu texts used the term śūnya (zero) to indicate the empty column on the abacus.^[29]

Japanese[edit]

In Japanese, the abacus is called soroban (算盤, そろばん, lit. 'Counting tray'), imported from China in the 14th century.^[30] It was probably in use by the working class a century or more before the ruling class started, as the class structure did not allow for devices used by the lower class to be adopted or used by the ruling class.^[31] The 1/4 abacus, which is suited to decimal calculation popular appeared circa 1930, and became widespread as the Japanese abandoned hexadecimal weight calculation which was still common in China.

Today's Japanese abacus is a 1:4 type, four-bead abacus was introduced from China in the Muromachi era. It adopts the form of the upper deck one bead and the bottom four beads. The top bead on the upper deck was equal to five and the bottom one is equal to one like the Chinese or Korean abacus, and the decimal number can be expressed, so the abacus is designed as one four abacus. The beads are always in the shape of a diamond. The quotient division is generally used instead of the division method; at the same time, in order to make the multiplication and division digits consistently use the division multiplication. Later, Japan had a 3:5 abacus called天三算盤, which is now the Ize Rongji collection of Shansi Village in Yamagata City. There were also had 2:5 beads abacus.With the four-bead abacus spread, it is also common to use Japanese abacus around the world. There are also improved Japanese abacus in various places. One of the Japanese-made abacus made in China is an aluminum frame plastic bead abacus. The file is next to the four beads, and the 'clearing' button, press the clearing button, immediately put the upper bead to the upper position, the lower bead is dialed to the lower position, immediately clearing, easy to use.

The abacus is still manufactured in Japan today even with the proliferation, practicality, and affordability of pocket electronic calculators. The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation. Using visual imagery of a soroban, one can arrive at the answer in the same time as, or even faster than, is possible with a physical instrument.^[32]

Korean[edit]

The Chinese abacus migrated from China to Korea around 1400 AD.^[18][33][34] Koreans call it jupan (주판), supan (수판) or jusan (주산).^[35]The four beads abacus( 1:4 ) was introduced to Korea Goryeo Dynasty from the China during Song Dynasty, later the five beads abacus (5:1) abacus was introduced to Korean from China during the Ming Dynasty.

Native American[edit]

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Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture.^[36] This Mesoamerican abacus used a 5-digit base-20 system.^[37]The word Nepōhualtzintzin [nepoːwaɬˈt͡sint͡sin] comes from Nahuatl and it is formed by the roots; Ne – personal -; pōhual or pōhualli[ˈpoːwalːi] – the account -; and tzintzin[ˈt͡sint͡sin] – small similar elements. Its complete meaning was taken as: counting with small similar elements by somebody. Its use was taught in the Calmecac to the temalpouhqueh[temaɬˈpoʍkeʔ], who were students dedicated to take the accounts of skies, from childhood.

The Nepōhualtzintzin was divided in two main parts separated by a bar or intermediate cord. In the left part there were four beads, which in the first row have unitary values (1, 2, 3, and 4), and in the right side there are three beads with values of 5, 10, and 15 respectively. In order to know the value of the respective beads of the upper rows, it is enough to multiply by 20 (by each row), the value of the corresponding account in the first row.

Altogether, there were 13 rows with 7 beads in each one, which made up 91 beads in each Nepōhualtzintzin. This was a basic number to understand, 7 times 13, a close relation conceived between natural phenomena, the underworld and the cycles of the heavens. One Nepōhualtzintzin (91) represented the number of days that a season of the year lasts, two Nepōhualtzitzin (182) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin (273) is the number of days of a baby's gestation, and four Nepōhualtzintzin (364) completed a cycle and approximate a year (11/4 days short). When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to the 18 in floating point, which calculated stellar as well as infinitesimal amounts with absolute precision, meant that no round off was allowed.

The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo,^[38] who in his wanderings throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them made in gold, jade, encrustations of shell, etc.^[39] There have also been found very old Nepōhualtzintzin attributed to the Olmec culture, and even some bracelets of Mayan origin, as well as a diversity of forms and materials in other cultures.

George I. Sanchez, 'Arithmetic in Maya', Austin-Texas, 1961 found another base 5, base 4 abacus in the Yucatán Peninsula that also computed calendar data. This was a finger abacus, on one hand 0, 1, 2, 3, and 4 were used; and on the other hand 0, 1, 2 and 3 were used. Note the use of zero at the beginning and end of the two cycles. Sanchez worked with Sylvanus Morley, a noted Mayanist.

The quipu of the Incas was a system of colored knotted cords used to record numerical data,^[40] like advanced tally sticks – but not used to perform calculations. Calculations were carried out using a yupana (Quechua for 'counting tool'; see figure) which was still in use after the conquest of Peru. The working principle of a yupana is unknown, but in 2001 an explanation of the mathematical basis of these instruments was proposed by Italian mathematician Nicolino De Pasquale. By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum.^[41]

Russian[edit]

The Russian abacus, the schoty (Russian: счёты, plural from Russian: счёт, counting), usually has a single slanted deck, with ten beads on each wire (except one wire, usually positioned near the user, with four beads for quarter-ruble fractions). Older models have another 4-bead wire for quarter-kopeks, which were minted until 1916. 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, 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 are of a different color from the other eight beads. Likewise, the left bead of the thousands wire (and the million wire, if present) may have a different color.

As a simple, cheap and reliable device, the Russian abacus was in use in all shops and markets throughout the former Soviet Union, and the usage of it was taught in most schools until the 1990s.^[42][43] Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia and likewise the mass production of Felix arithmometers since 1924 did not significantly reduce their use in the Soviet Union.^[44] The Russian abacus began to lose popularity only after the mass production of microcalculators had started in the Soviet Union in 1974. Today it is regarded as an archaism and replaced by the handheld calculator.

The Russian abacus was brought to France around 1820 by the mathematician Jean-Victor Poncelet, who served in Napoleon's army and had been a prisoner of war in Russia.^[45] The abacus had fallen out of use in western Europe in the 16th century with the rise of decimal notation and algorismic methods. To Poncelet's French contemporaries, it was something new. Poncelet used it, not for any applied purpose, but as a teaching and demonstration aid.^[46] The Turks and the Armenian people also used abacuses similar to the Russian schoty. It was named a coulba by the Turks and a choreb by the Armenians.^[47]

School abacus[edit]

Around the world, abacuses have been used in pre-schools and elementary schools as an aid in teaching the numeral system and arithmetic.

In Western countries, a bead frame similar to the Russian abacus but with straight wires and a vertical frame has been common (see image). It is still often seen as a plastic or wooden toy.

The wire frame may be used either with positional notation like other abacuses (thus the 10-wire version may represent numbers up to 9,999,999,999), or each bead may represent one unit (so that e.g. 74 can be represented by shifting all beads on 7 wires and 4 beads on the 8th wire, so numbers up to 100 may be represented). Teaching multiplication, e.g. 6 times 7 may be represented by shifting 7 beads on 6 wires. In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use.

The red-and-white abacus is used in contemporary primary schools for a wide range of number-related lessons. The twenty bead version, referred to by its Dutch name rekenrek ('calculating frame'), is often used, sometimes on a string of beads, sometimes on a rigid framework.^[48]

Neurological analysis[edit]

By learning how to calculate with abacus, one can improve one's mental calculation which becomes faster and more accurate in doing large number calculations. Abacus‐based mental calculation (AMC) was derived from the abacus which means doing calculation, including addition, subtraction, multiplication, and division, in mind with an imagined abacus. It is a high-level cognitive skill that run through calculations with an effective algorithm. People doing long-term AMC training show higher numerical memory capacity and have more effectively connected neural pathways.^[49][50] They are able to retrieve memory to deal with complex processes to calculate.^[51] The processing of AMC involves both the visuospatial and visuomotor processing which generate the visual abacus and perform the movement of the imaginary bead.^[52] Since the only thing needed to be remembered is the finial position of beads, it takes less memory and less computation time.^[52]

Renaissance abacuses gallery[edit]

Uses by the blind[edit]

An adapted abacus, invented by Tim Cranmer, called a Cranmer abacus is still commonly used by individuals who are blind. A piece of soft fabric or rubber is placed behind the beads so that they do not move inadvertently. This keeps the beads in place while the users feel or manipulate them. They use an abacus to perform the mathematical functions multiplication, division, addition, subtraction, square root and cube root.^[53]

Although blind students have benefited from talking calculators, the abacus is still very often taught to these students in early grades, both in public schools and state schools for the blind.^[54] Blind students also complete mathematical assignments using a braille-writer and Nemeth code (a type of braille code for mathematics) but large multiplication and long division problems can be long and difficult. The abacus gives blind and visually impaired students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine a very useful tool throughout life.^[53]

Binary abacus[edit]

The binary abacus is used to explain how computers manipulate numbers.^[55] The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in three separate rows. The beads represent a switch on the computer in either an 'on' or 'off' position.

See also[edit]

Notes[edit]

1. ^Both C. J. Gadd, a keeper of the Egyptian and Assyrian Antiquities at the British Museum, and Jacob Levy, a Jewish Historian who wrote Neuhebräisches und chaldäisches wörterbuch über die Talmudim und Midraschim [Neuhebräisches and Chaldean dictionary on the Talmuds and Midrashi] disagree with the 'dust table' theory.^[7]

Footnotes[edit]

1. ^ ^abcBoyer & Merzbach 1991, pp. 252–253
2. ^de Stefani 1909, p. 2
3. ^Gaisford 1962, p. 2
4. ^Lasserre & Livadaras 1976, p. 4
5. ^Klein 1966, p. 1
6. ^Onions, Friedrichsen & Burchfield 1967, p. 2
7. ^ ^abPullan 1968, p. 17
8. ^Huehnergard 2011, p. 2
9. ^ ^abBrown 1993, p. 2
10. ^Gove 1976, p. 1
11. ^Ifrah 2001, p. 11
12. ^Crump 1992, p. 188
13. ^Melville 2001
14. ^Carruccio 2006, p. 14
15. ^Smith 1958, pp. 157–160
16. ^Carr 2014
17. ^Ifrah 2001, p. 15
18. ^ ^abcWilliams 1997, p. 55
19. ^ ^abPullan 1968, p. 16
20. ^Williams 1997, pp. 55–56
21. ^Ifrah 2001, p. 17
22. ^Fernandes 2003
23. ^Pullan 1968, p. 18
24. ^Brown 2010, pp. 81–82
25. ^Brown 2011
26. ^Huff 1993, p. 50
27. ^Ifrah 2001, p. 18
28. ^Körner 1996, p. 232
29. ^Mollin 1998, p. 3
30. ^Gullberg 1997, p. 169
31. ^Williams 1997, p. 65
32. ^Murray 1982
33. ^Anon 2002
34. ^Jami 1998, p. 4
35. ^Anon 2013
36. ^Sanyal 2008
37. ^Anon 2004
38. ^Hidalgo 1977, p. 94
39. ^Hidalgo 1977, pp. 94–101
40. ^Albree 2000, p. 42
41. ^Aimi & De Pasquale 2005
42. ^Burnett & Ryan 1998, p. 7
43. ^Hudgins 2004, p. 219
44. ^Leushina 1991, p. 427
45. ^Trogeman & Ernst 2001, p. 24
46. ^Flegg 1983, p. 72
47. ^Williams 1997, p. 64
48. ^West 2011, p. 49
49. ^Hu, Yuzheng; Geng, Fengji; Tao, Lixia; Hu, Nantu; Du, Fenglei; Fu, Kuang; Chen, Feiyan (December 14, 2010). 'Enhanced white matter tracts integrity in children with abacus training'. Human Brain Mapping. 32 (1): 10–21. doi:10.1002/hbm.20996. ISSN1065-9471. PMID20235096.
50. ^Wu, Tung-Hsin; Chen, Chia-Lin; Huang, Yung-Hui; Liu, Ren-Shyan; Hsieh, Jen-Chuen; Lee, Jason J. S. (November 5, 2008). 'Effects of long-term practice and task complexity on brain activities when performing abacus-based mental calculations: a PET study'. European Journal of Nuclear Medicine and Molecular Imaging. 36 (3): 436–445. doi:10.1007/s00259-008-0949-0. ISSN1619-7070. PMID18985348.
51. ^Lee, J.S.; Chen, C.L.; Wu, T.H.; Hsieh, J.C.; Wui, Y.T.; Cheng, M.C.; Huang, Y.H. (2003). 'Brain activation during abacus-based mental calculation with fMRI: A comparison between abacus experts and normal subjects'. First International IEEE EMBS Conference on Neural Engineering, 2003. Conference Proceedings. pp. 553–556. doi:10.1109/CNE.2003.1196886. ISBN0-7803-7579-3.
52. ^ ^abChen, C.L.; Wu, T.H.; Cheng, M.C.; Huang, Y.H.; Sheu, C.Y.; Hsieh, J.C.; Lee, J.S. (December 20, 2006). 'Prospective demonstration of brain plasticity after intensive abacus-based mental calculation training: An fMRI study'. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 569 (2): 567–571. Bibcode:2006NIMPA.569..567C. doi:10.1016/j.nima.2006.08.101. ISSN0168-9002.
53. ^ ^abTerlau & Gissoni 2006
54. ^Presley & D'Andrea 2009
55. ^Good Jr. 1985, p. 34

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• Gullberg, Jan (1997). Mathematics: From the Birth of Numbers. Illustrated by Pär Gullberg. New York, NY: W. W. Norton & Company. ISBN978-0-393-04002-9.
• Hidalgo, David Esparza (1977). Nepohualtzintzin: Computador Prehispánico en Vigencia [The Nepohualtzintzin: An Effective Pre-Hispanic Computer] (in Spanish). Tlacoquemécatl, Mexico: Editorial Diana.
• Hudgins, Sharon (2004). The Other Side of Russia: A Slice of Life in Siberia and the Russian Far East. Eugenia & Hugh M. Stewart '26 Series on Eastern Europe. Texas A&M University Press. ISBN978-1-58544-404-5.
• Huehnergard, John, ed. (2011). 'Appendix of Semitic Roots, under the root ʾbq.'. American Heritage Dictionary of the English Language (5th ed.). Houghton Mifflin Harcourt Trade. ISBN978-0-547-04101-8.
• Huff, Toby E. (1993). The Rise of Early Modern Science: Islam, China and the West (1st ed.). Cambridge, UK: Cambridge University Press. ISBN978-0-521-43496-6.
• Ifrah, Georges (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. New York, NY: John Wiley & Sons, Inc. ISBN978-0-471-39671-0.
• Jami, Catherine (1998). 'Abacus (Eastern)'. In Bud, Robert; Warner, Deborah Jean (eds.). Instruments of Science: An Historical Encyclopedia. New York, NY: Garland Publishing, Inc. ISBN978-0-8153-1561-2.
• Klein, Ernest, ed. (1966). 'abacus'. A Comprehensive Etymological Dictionary of the English Language. I: A-K. Amsterdam: Elsevier Publishing Company.
• Körner, Thomas William (1996). The Pleasures of Counting. Cambridge, UK: Cambridge University Press. ISBN978-0-521-56823-4.
• Lasserre, Franciscus; Livadaras, Nicolaus, eds. (1976). Etymologicum Magnum Genuinum: Symeonis Etymologicum: Una Cum Magna Grammatica (in Greek and Latin). Primum: α — άμωσϒέπωϛ. Rome, Italy: Edizioni dell'Ateneo. LCCN77467964.
• Leushina, A. M. (1991). The development of elementary mathematical concepts in preschool children. National Council of Teachers of Mathematics. ISBN978-0-87353-299-0.
• Melville, Duncan J. (May 30, 2001). 'Chronology of Mesopotamian Mathematics'. St. Lawrence University. It.stlawu.edu. Archived from the original on January 12, 2014. Retrieved Jun 19, 2014.
• Mish, Frederick C., ed. (2003). 'abacus'. Merriam-Webster's Collegiate Dictionary (11th ed.). Merriam-Webster, Inc. ISBN978-0-87779-809-5.
• Mollin, Richard Anthony (September 1998). Fundamental Number Theory with Applications. Discrete Mathematics and its Applications. Boca Raton, FL: CRC Press. ISBN978-0-8493-3987-5.
• Murray, Geoffrey (July 20, 1982). 'Ancient calculator is a hit with Japan's newest generation'. The Christian Science Monitor. CSMonitor.com. Archived from the original on December 2, 2013. Retrieved July 31, 2014.
• Onions, C. T.; Friedrichsen, G. W. S.; Burchfield, R. W., eds. (1967). 'abacus'. The Oxford Dictionary of English Etymology. Oxford, UK: Oxford at the Clarendon Press.
• Presley, Ike; D'Andrea, Frances Mary (2009). Assistive Technology for Students who are Blind Or Visually Impaired: A Guide to Assessment. American Foundation for the Blind. p. 61. ISBN978-0-89128-890-9.
• Pullan, J. M. (1968). The History of the Abacus. New York, NY: Frederick A. Praeger, Inc., Publishers. ISBN978-0-09-089410-9. LCCN72075113.
• Reilly, Edwin D., ed. (2004). Concise Encyclopedia of Computer Science. New York, NY: John Wiley and Sons, Inc. ISBN978-0-470-09095-4.Missing or empty |title= (help)
• Sanyal, Amitava (July 6, 2008). 'Learning by Beads'. Hindustan Times.
• Smith, David Eugene (1958). History of Mathematics. Dover Books on Mathematics. 2: Special Topics of Elementary Mathematics. Courier Dover Publications. ISBN978-0-486-20430-7.
• Stearns, Peter N.; Langer, William Leonard, eds. (2001). 'The Encyclopedia of World History: Ancient, Medieval, and Modern, Chronologically Arranged'. The Encyclopedia of World History (6th ed.). New York, NY: Houghton Mifflin Harcourt. ISBN978-0-395-65237-4.
• Terlau, Terrie; Gissoni, Fred (July 20, 2006). 'Abacus: Position Paper'. APH.org. Archived from the original on December 2, 2013. Retrieved July 31, 2014.
• Trogeman, Georg; Ernst, Wolfgang (2001). Trogeman, Georg; Nitussov, Alexander Y.; Ernst, Wolfgang (eds.). Computing in Russia: The History of Computer Devices and Information Technology Revealed. Braunschweig/Wiesbaden: Vieweg+Teubner Verlag. ISBN978-3-528-05757-2.
• West, Jessica F. (2011). Number sense routines : building numerical literacy every day in grades K-3. Portland, Me.: Stenhouse Publishers. ISBN978-1-57110-790-9.
• Williams, Michael R. (1997). Baltes, Cheryl (ed.). A History of Computing technology (2nd ed.). Los Alamitos, CA: IEEE Computer Society Press. ISBN978-0-8186-7739-7. LCCN96045232.
• Yoke, Ho Peng (2000). Li, Qi and Shu: An Introduction to Science and Civilization in China. Dover Science Books. Courier Dover Publications. ISBN978-0-486-41445-4.

Further reading[edit]

• Fernandes, Luis (2013). 'The Abacus: A Brief History'. ee.ryerson.ca. Archived from the original on July 2, 2014. Retrieved July 31, 2014.
• Menninger, Karl W. (1969), Number Words and Number Symbols: A Cultural History of Numbers, MIT Press, ISBN978-0-262-13040-0
• Kojima, Takashi (1954), The Japanese Abacus: its Use and Theory, Tokyo: Charles E. Tuttle Co., Inc., ISBN978-0-8048-0278-9
• Kojima, Takashi (1963), Advanced Abacus: Japanese Theory and Practice, Tokyo: Charles E. Tuttle Co., Inc., ISBN978-0-8048-0003-7
• Stephenson, Stephen Kent (July 7, 2010), Ancient Computers, IEEE Global History Network, arXiv:1206.4349, Bibcode:2012arXiv1206.4349S, retrieved July 2, 2011
• Stephenson, Stephen Kent (2013), Ancient Computers, Part I - Rediscovery, Edition 2, ISBN978-1-4909-6437-9

External links[edit]

• Texts on Wikisource:
  • 'Abacus'. Encyclopædia Britannica (11th ed.). 1911.
  • 'Abacus', from A Dictionary of Greek and Roman Antiquities, 3rd ed., 1890.

Tutorials[edit]

• Heffelfinger, Totton & Gary Flom, Abacus: Mystery of the Bead - an Abacus Manual
• Stephenson, Stephen Kent (2009), How to use a Counting Board Abacus

Abacus curiosities[edit]

• Schreiber, Michael (2007), Abacus, The Wolfram Demonstrations Project
• Abacus in Various Number Systems at cut-the-knot

Crack For Autocad 2013

AutoCAD is a commercialcomputer-aided design (CAD) and drafting software application. Developed and marketed by Autodesk,^[1] AutoCAD was first released in December 1982 as a desktop app running on microcomputers with internal graphics controllers.^[2] Before AutoCAD was introduced, most commercial CAD programs ran on mainframe computers or minicomputers, with each CAD operator (user) working at a separate graphics terminal.^[3] Since 2010, AutoCAD was released as a mobile- and web app as well, marketed as AutoCAD 360.

AutoCAD is used in the industry, by architects, project managers, engineers, graphic designers, city planners and other professionals. It was supported by 750 training centers worldwide in 1994.^[1]

• 2Features
• 3Variants
• 4Ports

History[edit]

AutoCAD was derived from a program that began in 1977, and then released in 1979^[4] called Interact CAD,^[5][6][7] also referred to in early Autodesk documents as MicroCAD, which was written prior to Autodesk's (then Marinchip Software Partners) formation by Autodesk cofounder Michael Riddle.^[8][9]

The first version by Autodesk was demonstrated at the 1982 Comdex and released that December. AutoCAD supported CP/M-80 computers.^[10] As Autodesk's flagship product, by March 1986 AutoCAD had become the most ubiquitous CAD program worldwide.^[11] The 2020 release marked the 34th major release of AutoCAD for Windows. The 2019 release marked the ninth consecutive year of AutoCAD for Mac. The native file format of AutoCAD is .dwg. This and, to a lesser extent, its interchange file format DXF, have become de facto, if proprietary, standards for CAD data interoperability, particularly for 2D drawing exchange.^{[citation needed]} AutoCAD has included support for .dwf, a format developed and promoted by Autodesk, for publishing CAD data.

Features[edit]

Compatibility with other software[edit]

ESRI ArcMap 10 permits export as AutoCAD drawing files. Civil 3D permits export as AutoCAD objects and as LandXML. Third-party file converters exist for specific formats such as Bentley MX GENIO Extension, PISTE Extension (France), ISYBAU (Germany), OKSTRA and Microdrainage (UK);^[12] also, conversion of .pdf files is feasible, however, the accuracy of the results may be unpredictable or distorted. For example, jagged edges may appear. Several vendors provide online conversions for free such as Cometdocs.autoCAD commonly use in all purposes.

Language[edit]

Auto CAD and AutoCAD LT are available for English, German, French, Italian, Spanish, Korean, Chinese Simplified, Chinese Traditional, Brazilian Portuguese, Russian, Czech, Polish and Hungarian, Albanian (also through additional language packs).^[13] The extent of localization varies from full translation of the product to documentation only. The AutoCAD command set is localized as a part of the software localization.

Extensions[edit]

AutoCAD supports a number of APIs for customization and automation. These include AutoLISP, Visual LISP, VBA, .NET and ObjectARX. ObjectARX is a C++ class library, which was also the base for:

• products extending AutoCAD functionality to specific fields
• creating products such as AutoCAD Architecture, AutoCAD Electrical, AutoCAD Civil 3D
• third-party AutoCAD-based application

There are a large number of AutoCAD plugins (add-on applications) available on the application store Autodesk Exchange Apps.^[14]AutoCAD's DXF, drawing exchange format, allows importing and exporting drawing information.

Vertical integration[edit]

Autodesk has also developed a few vertical programs for discipline-specific enhancements such as:

• AutoCAD Advance Steel
• AutoCAD CIVIL 3D
• AutoCAD Electrical
• AutoCAD ecscad
• AutoCAD Map 3D
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• AutoCAD MEP
• AutoCAD Structural Detailing
• AutoCAD Utility Design
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Since AutoCAD 2019 several verticals are included with AutoCAD subscription as Industry-Specific Toolset.

For example, AutoCAD Architecture (formerly Architectural Desktop) permits architectural designers to draw 3D objects, such as walls, doors, and windows, with more intelligent data associated with them rather than simple objects, such as lines and circles. The data can be programmed to represent specific architectural products sold in the construction industry, or extracted into a data file for pricing, materials estimation, and other values related to the objects represented.

Additional tools generate standard 2D drawings, such as elevations and sections, from a 3D architectural model. Similarly, Civil Design, Civil Design 3D, and Civil Design Professional support mode and linking to third-party cloud-based storage such as Dropbox. Having evolved from Flash-based software, AutoCAD 360 uses HTML5 browser technology available in newer browsers including Firefox and Google Chrome.

AutoCAD WS began with a version for the iPhone and subsequently expanded to include versions for the iPod Touch, iPad, Android phones, and Android tablets.^[17] Autodesk released the iOS version in September 2010,^[18] following with the Android version on April 20, 2011.^[19] The program is available via download at no cost from the App Store (iOS), Google Play (Android) and Amazon Appstore (Android).

In its initial iOS version, AutoCAD WS supported drawing of lines, circles, and other shapes; creation of text and comment boxes; and management of color, layer, and measurements — in both landscape and portrait modes. Version 1.3, released August 17, 2011, added support for unit typing, layer visibility, area measurement and file management.^[16] The Android variant includes the iOS feature set along with such unique features as the ability to insert text or captions by voice command as well as manually.^[19] Both Android and iOS versions allow the user to save files on-line — or off-line in the absence of an Internet connection.^[19]

In 2011, Autodesk announced plans to migrate the majority of its software to 'the cloud', starting with the AutoCAD WS mobile application.^[20]

According to a 2013 interview with Ilai Rotbaein, an AutoCAD WS Product Manager for Autodesk, the name AutoCAD WS had no definitive meaning, and was interpreted variously as Autodesk Web Service, White Sheet or Work Space.^[21]

Student versions[edit]

AutoCAD is licensed, for free, to students, educators, and educational institutions, with a 36-month renewable license available. The student version of AutoCAD is functionally identical to the full commercial version, with one exception: DWG files created or edited by a student version have an internal bit-flag set (the 'educational flag'). When such a DWG file is printed by any version of AutoCAD (commercial or student) older than AutoCAD 2014 SP1 or AutoCAD 2019 and newer, the output includes a plot stamp/banner on all four sides. Objects created in the Student Version cannot be used for commercial use. Student Version objects 'infect' a commercial version DWG file if they are imported in versions older than AutoCAD 2015 or newer than AutoCAD 2018.^[22]

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Ports[edit]

Windows[edit]

AutoCAD is a software package created for Windows and usually, any new AutoCAD version supports the current Windows version and some older ones. AutoCAD 2016 to 2020 support Windows 7 up to Windows 10.^[23]

Mac[edit]

Autodesk stopped supporting Apple's Macintosh computers in 1994. Over the next several years, no compatible versions for the Mac were released. In 2010 Autodesk announced that it would once again support Apple's Mac OS X software in the future.^[24] Most of the features found in the 2012 Windows version can be found in the 2012 Mac version. The main difference is the user interface and layout of the program. The interface is designed so that users who are already familiar with Apple's macOS software will find it similar to other Mac applications.^[18] Autodesk has also built in various features in order to take full advantage of Apple's Trackpad capabilities as well as the full-screen mode in Apple's OS X Lion.^[17][18] AutoCAD 2012 for Mac supports both the editing and saving of files in DWG formatting that will allow the file to be compatible with other platforms besides the OS X.^[17] AutoCAD 2019 for Mac requires Apple OS X v10.11 (El Capitan) or later.

AutoCAD LT 2013 was available through the Mac App Store for $899.99. The full-featured version of AutoCAD 2013 for Mac, however, wasn't available through the Mac App Store due to the price limit of $999 set by Apple. AutoCAD 2014 for Mac was available for purchase from Autodesk's Web site for $4,195 and AutoCAD LT 2014 for Mac for $1,200, or from an Autodesk Authorized Reseller.^[24] The latest version available for Mac is AutoCAD 2019 as of December 2018. As of 2019, no Autocad release is listed for purchase on the MacOS App Store.

See also[edit]

• LibreCAD - cross-platform, free and open source 2D CAD
• FreeCAD - cross-platform, free and open source 3D CAD
• BRL-CAD - cross-platform, free and open source 3D CAD

References[edit]

1. ^ ^ab'Autodesk, Inc'. FundingUniverse. Lendio. 2012. Retrieved 29 March 2012.
2. ^'Chapter 8 : Autodesk and AutoCAD'(PDF). Cadhistory.net. Retrieved 2016-03-30.
3. ^'Chapter 2 : A Brief Overview of the History of CAD'(PDF). Cadhistory.net. Retrieved 2016-03-30.
4. ^Riddle, Michael. 'About'. Retrieved 24 January 2014. I’ve been building CAD products for over 29 years now, starting with Interact for the Marinchip 9900 released back in 1979, one of the first PC-based CAD programs available. Interact went on to become the architectural basis for the early versions of AutoCAD. I was one of the original 18 founders of that company.
5. ^http://www.studiodaily.com/2012/01/the-fascinating-story-of-how-autodesk-came-to-be-part-1/
6. ^http://www.michaelriddle.com/?page_id=2
7. ^http://www.retrothing.com/2007/05/mike_riddles_pr.html
8. ^Walker, John (1 May 1982). 'Information letter #5'. Retrieved 24 January 2014.
9. ^Yare, Evan (17 Feb 2012). 'AutoCAD's Ancestor'. 3D CAD World. Retrieved 24 January 2014.
10. ^One Company's CAD Success Story, InfoWorld, 3 December 1984, retrieved 19 July 2014
11. ^'Part 2 CAD/CAM/CAE', 25 Year retrospective, Computer Graphics World, 2011, retrieved 29 March 2012
12. ^'AutoCAD Civil 3D 2011 Drawing Compatibility'(PDF). AutoCAD Civil 3D 2011 User's Guide. Autodesk. April 2010. pp. 141–142. Retrieved January 29, 2013.
13. ^'AutoCAD 2016 Language Packs | AutoCAD | Autodesk Knowledge Network'. knowledge.autodesk.com. Retrieved 2016-11-03.
14. ^'AutoCAD Exchange Apps'. Autodesk. Retrieved 11 August 2013.
15. ^'Questions and Answers'(PDF). Images.autodesk.com. Retrieved 2016-03-30.
16. ^ ^abAutodesk. 'AutoCAD WS'. iTunes Preview. Apple. Retrieved 30 September 2011.
17. ^ ^abcOzler, Levent. 'AutoCAD for Mac and AutoCAD WS application for iPad and iPhone'. Dexigner. Dexigner. Retrieved 30 September 2011.
18. ^ ^abcOzler, Levent. 'AutoCAD for Mac 2012: Built for Mac OS X Lion'. Dexigner. Dexigner. Retrieved 30 September 2011.
19. ^ ^abcOzler, Levent. 'AutoCAD WS for Android'. Dexigner. Dexigner. Retrieved 30 September 2011.
20. ^Thomson, Iain. 'Autodesk Shifts Design Apps to the Cloud'. The A Register. The A Register. Retrieved 30 September 2011.
21. ^'AutoCAD WS: Moving Forward'. Augi Autodesk Users Group International, January 29th, 2013. Retrieved 26 April 2013.
22. ^'Overview of Plotting'. Retrieved 19 March 2016.
23. ^'System requirements for AutoCAD 2016 | AutoCAD | Autodesk Knowledge Network'. Knowledge.autodesk.com. 2015-12-16. Retrieved 2016-03-19.
24. ^ ^abClark, Don (16 August 2011). 'Autodesk Adopts Apple App Store for Mac Software'. The Wall Street Journal. Retrieved 30 September 2011.

Further reading[edit]

• Hurley, Shaan. 'AutoCAD Release History'. Between the lines.
• 'Mike Riddle & the Story of Interact, AutoCAD, EasyCAD, FastCAD & more'. DigiBarn Computer Museum. Retrieved 12 November 2016.
• 'About'. Michael Riddle's Thoughts. Retrieved 12 November 2016.
• Plantec, Peter (7 January 2012). 'The Fascinating Story of How Autodesk Came to Be (Part 1)'. Studio Daily. Access Intelligence.
• Grahame, James (17 May 2007). 'Mike Riddle's Prehistoric AutoCAD'. Retro Thing.

External links[edit]

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