Abacus and Abacus types (Frame Count - Calculator Manual)
The Abacus, an ancient tool
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still used today
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The Abacus, an ancient tool
CalculationManual,
still used today
Photo Source
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The Abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for the exercise of arithmetic processes. Today, nomograms are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones, then moved into the grooves in the sand or on tablets of wood, stone or metal. The abacus was for centuries before the adoption of the modern system of numerals written and is still widely used by traders, merchants and dependent on Asia, Africa andelsewhere. The user of an abacus is called a abacist.
Etymology of Abacus - (Abacus and Abacus types Frame Count)
The use of the word abacus dates back to dates before 1387 AD, when an Englishman working in the middle of America borrowed the word to describe an abacus sandboarding. The word came from America Άβακός Abaka, the Greek genitive form Άβαξ abax ("calculating table"), Hebrew Abaqa (אבק), "dust." The preferred plural of abacus is a subject of disagreement, both with an abacus and abacus in use.
Mesopotamian Abacus - (Abacus and Abacus types Frame Count)
The period 2700-2300 A.C. Saw the first appearance of the Sumerians Abacus, a table of successive columns which delimited the successive orders of magnitude of their sexagesimal number system.
Some scholars point to a character from the Babylonian cuneiform may have derived from a representation of the abacus. Carrucci is the belief (and other scholars of ancient Babylon) that Old Babylonian "may have used the abacus for the operations of addition and subtraction, however, this primitive device proved difficult to use for more complex calculations."
Egyptian Abacus - (Abacus and Abacus types Frame Count)
The use of the abacus in Ancient Egypt is mentioned by the Greek historian Herodotus, who writes that the hard way of using this by the Egyptians was opposite when compared to the Greek method. Archaeologists have found ancient disks of various sizes that are believed to have been used as counters. However, wall depictions of this instrument have not been discovered, casting doubt on the extent to which this instrument was used.
Iranian-Persian Abacus - (Abacus and Abacus types Frame Count)
During the Achaemenid Persian empire around 600 BC, Iranians began to use the abacus. In the Parthian Empire, Sassanid and Iranians, scholars concentrated on exchanging knowledge and inventions of the countries around them: India, China and the Roman Empire, it is believed that expanded into other countries.
Greek Abacus - (Abacus and Abacus types Frame Count)
The first archaeological evidence of the use of the Greek abacus dates to the fifth century BC. Greek abacus was a wooden board or marble, pre-set with small counters of wood or metal for mathematical calculations. The Greek abacus is believed to be used by Achaemenid Persia, the Etruscan civilization, ancient Rome, the French Revolution and to the Western Christian world.
A tablet found on the Greek island of Salamis in 1846 AD, dates back to 300 BC, making it the oldest counting board discovered so far. It is a white marble 149 cm (59 inches) long, 75 cm (30 inches) wide and 4.5 cm (2 inches) thick, about which there are 5 groups of markings. The center of the tablet is a set of 5 parallel lines equally divided by a vertical line topped with a semicircle at the intersection of the horizontal line over the bottom and one vertical line. Under 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 a semicircle at the top of the intersection, and the third, sixth and ninth of these lines are marked with a cross that intersects the vertical line.
Roman Abacus - (Abacus and Abacus types Frame Count)
The normal method of calculation in ancient Rome and Greece, was moving chips on a flat table. Originally pebbles, stones, were used. Later, and in medieval Europe, Jetons been made. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. This system of 'casting against "continued in the last Roman Empire and in medieval Europe, and persisted in limited use in the nineteenth century.
Writing in the first century BC, Horace refers to the wax abacus, a table covered with a thin layer of black wax in the columns and figures were inscribed using a stylus.
An example of the archaeological evidence of Roman abacus, shown here in the reconstruction, dates from the first century AD It has eight time slots to five counts of eight slots each, shorter than one or no beads in each. The groove marked I indicates units, X tens, and so on until millions of people. The accounts in the short slots denote five years and 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 can be used for marking Roman ounces.
Chinese Abacus - (Abacus and Abacus types Frame Count)
The Chinese abacus, known as the SUANP (算盘, lit. "Countinggeneralmente rounded and made of a hardwood. The accounts are counted by moving them up or down the beam. If you move towards the beam, account value. If you go, do not take into account their value. SUANP can be returned to the starting position instantly by a quick movement on the horizontal axis to spin all the beads off the horizontal bar in the center.
Suanpans can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficiently. SUANP techniques have been developed to do multiplication, division, addition, subtraction, square root and high speed operations. There are schools that teach students how to use it.
In the famous long trip along the river during the Qingming Festival painted by Zhang Zeduan (1085-1145 AD), Song Dynasty (960-1297 AD), a SUANP is clearly seen lying beside an account book and the prescription at the counter of an apothecary's (Feibao).
The similarity of the Roman abacus to the Chinese abacus, suggests it may have inspired others, and there is some evidence of a business relationship between the Roman Empire and China. However, no direct connection can prove it, and that similarity of the abacus may be coincidental, both ultimately derive from having five fingers on each hand. When the Roman model (like most modern Japanese) has 4 plus 1 bead per decimal, the standard SUANP has 5 plus 2, allowing use with the hexadecimal numbering system. Instead of running on wires as in the Japanese and Chinese models, the accounts of the Roman model run in grooves, presumably making arithmetic calculations can be much slower.
Another possible source is SUANP: Chinese counting rods, which operated with a decimal system but lacked the concept of zero as a placeholder. The zero was probably introduced by the Chinese in the Tang Dynasty (618-907 AD) due to travel in the Indian Ocean and the Middle East would have provided direct contact with India, enabling them to acquire the concept of zero and decimal point in India for traders and mathematicians.
The Abacus in India - (Abacus and Abacus types Frame Count)
First century sources, such as Abhidharmakosa describes the knowledge and use of abacus in India. Around the fifth century, employees in India found new ways to record the contents of the Abacus "Abacus." Hindu texts use the term shunya (zero) to indicate the empty column of the abacus.
Japanese Soroban Abacus - (Abacus and Abacus types Frame Count)
It is called in Japanese Soroban Abacus (算盘, そろ ばん, lit. "Counting tray") imported from China around 1600. On 4 abacus appeared circa 1930, which is preferred and is still manufactured in Japan today, including proliferation, viability and adsequibilidad pocket electronic calculators. Soroban use in Japan is still taught in primary schools as part of mathematics.
The Abacus Korean - (Abacus and Abacus types Frame Count)
The Chinese abacus migrated from China to Korea around 1400 BC In Korea they call Jupana (주판), Supan (수판) or Jusan (주산).
Native American Abacus - (Abacus and Abacus types Frame Count)
Some sources mention the use of an abacus called nepohualtzintzin in ancient Mayan culture. The Mesoamerican abacus used a 5-20 digit base of the system. Nepohualtzintzin word comes from the Nahuatl and consists of the roots, Ne - personal -; pohual or pohualli - count - and Tzintzin - small similar elements. Its full meaning is taken as small elements have someone similar. Its use was taught in the "Kalmekak" to "temalpouhkeh" who were dedicated students to take account of the heavens, since childhood. Unfortunately, the Nepohualtzintzin and its teaching were among the victims of the destruction of conquest, when a diabolical origin was attributed to them properties after observing the tremendous accuracy and speed of calculation.
This tool is based on the calculation vigesimal (base 20). For the Aztecs, the count of 20 years was completely natural, since the use of sandals (native sandals) allowed them to also use your toes to do calculations. Thus, the amount of 20 meant to them a complete human being. The Nepohualtzintzin is divided into two main parts separated by an intermediate rod or cable. On the left there are four balls in the first row have unitary values (1, 2, 3 and 4) and on the right side there are three balls, with values of 5, 10 and 15, respectively. To know the value of the respective accounts of the upper ranks, is multiplied by 20 (for each line), the value of the account in the first row.
In total, there are 13 rows with 7 beads in each, representing 91 balls in each Nepohualtzintzin. This is a base number to understand the close relationship between the accounts accurately designed and natural phenomena. This is for a Nepohualtzintzin (91) represents the number of days that a season lasts two Nepohualtzitzin (182) is the number of days in the maize cycle, from planting to harvest, three Nepohualtzintzin (273) is the number of days of gestation of a baby, and four Nepohualtzintzin (364) cycles and about a year (fourth short days). It is worth mentioning that the Nepohualtzintzin, amounts in the range of 10 to 18 can be calculated, with floating point, which allows calculating stellar and infinitesimal quantities with absolute precision.
The rediscovery of the maestro Nepohualtzintzin David Esparza Hidalgo, who in his wanderings across Mexico has found several engravings and paintings of this instrument and has reconstructed several of them in gold, jade, shell inlay, etc. We also found very old Nepohualtzintzin attributed to the Olmec culture, and even some bracelets of Mayan origin, as well as a variety of forms and materials in other cultures.
The quipu of the Incas was a system of knotted strings used to record numerical data and advanced counting sticks but not used for calculations. The calculations were performed using a Yupanqui (Quechua for "counting tool", which was still in use after the conquest of Peru. The working principle of a yupanas is unknown, but in 2001 an explanation of the mathematical basis of these instruments was given by the Italian mathematician Nicolino De Pasquale. By comparing the form of several yupanas, researchers found that the calculations were based on the use of the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20 and 40 as place values for different fields in the instrument. Using the Fibonacci sequence would maintain the number of grains within any area of a minimum.
Russian Abacus - (Abacus and Abacus types Frame Count)
The Russian abacus, the schety (счёты) usually has a single pitched roof, with ten beads on each wire (except one wire which has four beads, for quarter-ruble fractions. This cable usually appears in the user). (Older models have another piece of wire-4 for the quarter kopeks, which were minted until 1916.)
The Russian abacus is often used vertically, with wires from left to right in the form of a book. The cables are generally inclined to bulge upward in the center, to keep accounts covering any of the parties. It is clarified that all grains move to the right. During manipulation, beads are moved to the left. For easier viewing, the middle 2 balls on each wire (5 and 6 ball) are usually a different color from the other eight counts. Similarly, the left pull the thread of thousands (and the power of millions of dollars, if present) may have a different color.
As cheap and simple device effectively, the Russian abacus was in use in all stores and markets throughout the former Soviet Union, and the use of it is taught in most schools until the 1990's. Although the 1874 invention of the mechanical calculator, Arithmometer Odhner, they had not replaced in Russia and the mass production of arithmometers Felix since 1924 did not significantly reduce its use in the Soviet Union. The Abacus of Russia began to lose popularity until after Microcalculators mass production that had begun in the Soviet Union in 1974. Today it is regarded as an archaism and replaced by hand-held calculator.
The Russian abacus was brought to France around 1820 by the mathematician Jean-Victor Poncelet, who served the Napoleonic army who in turn had been a prisoner of war in Russia. The abacus had fallen into disuse in western Europe in the sixteenth century with the advent of decimal notation and algorithmic methods. For contemporary French Poncelet, was something new. Poncelet is used, not applied for any purpose, but as a lesson and show support.
School Abacus - (Abacus and Abacus types Frame Count)
Worldwide, the abacus has been used in preschools and primary schools as a teaching aid to the numbering system and calculation.
In Western countries, a framework similar to the abacus beads Russian, but with straight wires and a vertical frame has been common. It is still often seen as a toy plastic or wood.
This type of Abacus is often used to represent numbers without the use of place value. Each bead and wire, each has the same value and used in this way can represent numbers to 100.
Uses of the Abacus for the Blind - (Abacus and Abacus types Frame Count)
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 accounts that do not move inadvertently. This keeps the balls in place while the users feel to manipulate. They use an abacus to perform mathematical functions of multiplication, division, addition, subtraction, square root and cube root.
Although blind students have benefited from voice calculators, the abacus is still very often the preferred education for these students in early grades, both public schools and private schools for the blind.
The abacus teaches math skills that can never be replaced with talking calculators and is an important learning tool for blind students. Blind students also complete math tasks using a braille-writer and Nemeth code (a type of braille code for math) but large multiplication and division problems can eventually be long and difficult.
Abacus for the blind and visually impaired, gives students a tool to calculate the mathematical problems that is equal to the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people can find this machine as a tool number 1 and also very useful for a lifetime.
Binary Abacus - (Abacus and Abacus types Frame Count)
The binary abacus is used to explain how computers internally manipulate numbers. The abacus shows the amount of numbers, letters and signs that can be stored in a binary system on a computer, or via ASCII. The device consists of a series of accounts in parallel wires arranged in three distinct rows. The accounts represent a change in the computer either in an "on-on" or an "off-off."
