Abacus Calculating

abacus abacus: the units are placed at the top of the lower stem, the multiples of five in the bottom of the upper stem, the number reads so in the middle of the abacus, each column can represent numbers from 0 to 15 for the deferral of deductions multiples of 5.

An abacus (from the Latin and in Greek meaning "table dust") is the name given to any mechanical instrument facilitating the plane calculation.

List of tables

In the family of graphs can be classified

• the abacus on which we draw: the Greek abacus
• abacus-counter using pebbles or tokens: Egyptian or Roman abacus
• the abacus with balls sliding on rods: the great family of ball machines
• The abacus consists of a tray and slide strip, known as the sticks Napier

Overview of the history charts

In the history of counting , writing numbers did not help in general calculations. Surveyors and accountants have needed tools to help them calculate.

Stones

The easiest way is to use stones arranged on the ground. In Abyssinia (former name of Ethiopia ), for example, it was customary for warriors to battle to fight to deposit a pebble on a pile, he retired to Pebble returning from combat. The number of stones removed not possible to determine the number of deaths in combat. This extremely simple, however, has its limits. He had to complete the device.

But very long ago, the arithmetic unit was the stone or pebble, calculus in Latin (even when he substituted the sticks easier to draw, which later led to the invention of written numbers). This Latin term is also the origin of the word calculation (unused in its original meaning in medicine).

It is thus seen to grow successively input uses or more tables or charts:

"This instrument was used by peoples widely separated as the Etruscans , the Greeks , the Egyptians , the Indians , the Chinese and Mexican and they may think it was invented independently in different places ^{Greek Abacus}

The word abacus, the Greeks: ABAX, Akos (tablets used to calculate) becomes: among Roman abacus. It consisted of a table covered with sand on which we draw with a stylus, the calculations can be deleted as and when smoothing with the hand .

From this original chart-chart, the numbers will be born Phoenician, then a side Greek and Roman figures arising from the adaptation to their respective alphabet charts improved by the Phoenicians and other Semitic Assyrian side figures and Indian (should note that the zero point) and Arab-Indian (where zero is a circle) and late-Arab figures of modern European.

The abacus Greco-Phoenician is actually quite similar systems with counting sticks traditionally used by those who do not expect, or want to measure time using sticks that does not clear, but that it may strike, underline, circle ... This original system is still universally known commonly used today to count the points in a game, because it is faster and more efficient than scratch and rewrite all the numbers.

Chinese Abacus

The Chinese and Japanese do with the chart not only simple operations, but even the extraction of square roots. The disadvantage of the method is that verification is impossible

Abacus India

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Abacus Mexican

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Roman Abacus

reconstruction of a Roman abacus

This is a table divided into several columns, each column represents a power of 10. It further provides that the shingle is deposited in the columns of his choice. The Romans did not have an entry in decimal. However, their practice of the chart shows that they possessed the principle. Subsequently, the abacus has enriched checkboxes above each column representing 5 units of the combined power of 10.

The principle of addition and subtraction is easy to understand. The transfer is done by replacing the selected 10 pebbles in a column by a wheel of the next column (and vice versa).

The proliferation was a bit more complicated. You could choose to, add as many times as it was the starting number, or use the practice of duplicating the method of Egyptian multiplication.

Roman Abacus Mobile

Until the ^first century , the abacus was therefore difficult to transport furniture. The idea then came to build a metal plate to replace the columns with parallel grooves and slide into the grooves of the buttons the same size. We are getting closer then the abacus.

Gerbert d'Aurillac and the quarrel abaci cons algorism

Where in ^the tenth century , Gerbert of Aurillac (later to become Pope Sylvester II ) reports the Arabic numerals of his three-year stay in Spain in the mid-Muslims. He introduced a new chart, using figures. This chart will disappear soon after his death.

During the Crusades ( ^XI - XIII ^century ), the West became familiar willy-nilly with the calculation algorithms. Clerics income of the Crusades with decimal system of writing were the driving forces behind its facility in France. Arabic numerals and calculations they make possible are described in the Liber Abaci by Leonardo of Pisa. The computing system by the abacus still persist until the French Revolution and the opponent abaca, abacus calculation with favor, and ALGOR, developing algorithmic calculations described by the Arabs. We can talk about it the English title of Chancellor of the Exchequer to the Minister of Finance in England, meaning chessboard abacus, calculating taxes is still doing until the eighteenth ^century with an abacus.

The abacus disappears after the Revolution , with the advent of the metric system and cheap paper, and the development of new methods, requiring more than scratch the figures being calculated , the algorithmic method.

From the French Revolution to the Present

Japanese Soroban

The decimal spreads for all calculations, but shows its limitations and weaknesses in the calculations rather complex. We must now do better. To make simpler products, quotients, calculating sines and cosines , we invent numerical tables and slide rules. At work, the graphs or tables of correspondences multiply. But the calculation by hand is tedious. We are looking to automate. It then enters the automatic calculation date which is usually the invention of Pascal ( Blaise Pascal , 1646 ).

Gallery

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  Margarita Philosophica, writes the edition of 1508

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  Wooden abacus, probably in Strasbourg ^References

  1. Walter William Rouse Ball, A Short Account of The History of Mathematics, Section Abacus edition (2001), Dover Publications, p. 123-126 ( ISBN 1402700539 )
  2. Encyclopedic dictionary X volumes, 1982, Vol.I, p. 6 ( ISBN 2031023012 )
  3. encyclopedic dictionary, 1982, p. 6, op.
  4. Alain Schrling, Counting tokens, pp. 37-45

  See also

  Related articles

  • Technical knowledge
  • Soroban
  • Abacus
  • SuanPan
  • Stchoty
  • Mental arithmetic
  • Anshan

  Bibliography

  • Georges Ifrah , Universal History of Numbers.
  • Sylvain Gouguenheim Aristotle at Mont Saint-Michel p.64
  • Walter William Rouse Ball , A Short Account of The History of Mathematics, 2001, Dover, ( ISBN 1402700539 )
  • Larousse encyclopedia in ten volumes , 1982, vol. I, ( ISBN 2031023012 )
  • Alain Schrliger Counting with stones, the basic calculation on the abacus in ancient Greek PPUR , 2001
  • Alain Schrliger Counting with chips, tables and tables to calculate account of the Middle Ages to the Revolution, PPUR , 2003

  External Links

  • Use of abacus token in a land in the fourteenth ^century
  • Experimental approach charts and Roman Gerbert Canadian educational site on the teaching of mathematics through play
  • FFSA , French Federation of Soroban and other charts.

  • Mathematics Portal

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