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The abacus is still manufactured in Japan 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 can complete a calcul... |
Korea |
The Chinese abacus migrated from China to Korea around 1400 AD. Koreans call it jupan (주판), supan (수판) or jusan (주산). The four-beads abacus (1:4) was introduced during the Goryeo Dynasty. The 5:1 abacus was introduced to Korea from China during the Ming Dynasty. |
Native America |
Some sources mention the use of an abacus called a nepohualtzintzin in ancient Aztec culture. This Mesoamerican abacus used a 5-digit base-20 system. The word Nepōhualtzintzin comes from Nahuatl, formed by the roots; Ne – personal -; pōhual or pōhualli – the account -; and tzintzin – small similar elements. Its comp... |
The Nepōhualtzintzin was divided into two main parts separated by a bar or intermediate cord. In the left part were four beads. Beads in the first row have unitary values (1, 2, 3, and 4), and on the right side, three beads had values of 5, 10, and 15, respectively. In order to know the value of the respective beads o... |
The device featured 13 rows with 7 beads, 91 in total. This was a basic number for this culture. It had a close relation to 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 ... |
The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo, who in his travels throughout Mexico found diverse engravings and paintings of this instrument and reconstructed several of them in gold, jade, encrustations of shell, etc. Very old Nepōhualtzintzin are attributed to the Olme... |
Sanchez wrote in Arithmetic in Maya that another base 5, base 4 abacus had been found 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 cy... |
The quipu of the Incas was a system of colored knotted cords used to record numerical data, 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 o... |
Russia |
The Russian abacus, the schoty (, plural from , counting), usually has a single slanted deck, with ten beads on each wire (except one wire 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, wi... |
The Russian abacus was in use in shops and markets throughout the former Soviet Union, and its usage was taught in most schools until the 1990s. Even the 1874 invention of mechanical calculator, Odhner arithmometer, had not replaced them in Russia; according to Yakov Perelman. Some businessmen attempting to import calc... |
The Russian abacus was brought to France around 1820 by mathematician Jean-Victor Poncelet, who had served in Napoleon's army and had been a prisoner of war in Russia. 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 co... |
School abacus |
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 is common (see image). |
The wireframe 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 (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). In t... |
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, either on a string of beads or on a rigid framework. |
Feynman vs the abacus |
Physicist Richard Feynman was noted for facility in mathematical calculations. He wrote about an encounter in Brazil with a Japanese abacus expert, who challenged him to speed contests between Feynman's pen and paper, and the abacus. The abacus was much faster for addition, somewhat faster for multiplication, but Feynm... |
Neurological analysis |
Learning how to calculate with the abacus may improve capacity for mental calculation. Abacus-based mental calculation (AMC), which was derived from the abacus, is the act of performing calculations, including addition, subtraction, multiplication, and division, in the mind by manipulating an imagined abacus. It is a h... |
Renaissance abacuses |
Binary abacus |
The binary abacus is used to explain how computers manipulate numbers. 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 i... |
Visually impaired users |
An adapted abacus, invented by Tim Cranmer, and called a Cranmer abacus is commonly used by visually impaired users. A piece of soft fabric or rubber is placed behind the beads, keeping them in place while the users manipulate them. The device is then used to perform the mathematical functions of multiplication, divisi... |
Although blind students have benefited from talking calculators, the abacus is often taught to these students in early grades. Blind students can 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 are... |
See also |
Chinese Zhusuan |
Chisanbop |
Logical abacus |
Mental abacus |
Napier's bones |
Sand table |
Slide rule |
Soroban |
Suanpan |
Notes |
Footnotes |
References |
Reading |
External links |
Tutorials |
Min Multimedia |
Abacus curiosities |
Abacus in Various Number Systems at cut-the-knot |
Java applet of Chinese, Japanese and Russian abaci |
An atomic-scale abacus |
Examples of Abaci |
Aztex Abacus |
Indian Abacus |
Mathematical tools |
Chinese mathematics |
Egyptian mathematics |
Greek mathematics |
Indian mathematics |
Japanese mathematics |
Roman mathematics An acid is a molecule or ion capable of either donating a proton (i.e., hydrogen ion, H+), known as a Brønsted–Lowry acid, or, capable of forming a covalent bond with an electron pair, known as a Lewis acid. |
The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents. A Brønsted or Arrhenius acid usually cont... |
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