Thursday, 9 June 2011

The Abacus

The early Greeks used to design small trays and cover the bottom with sand to help hold pebbles steady when they were calculating. The Greek word for these trays and in general for round trays and large platters was abax and this became our word for abacus. The word may have been influenced by the semitic word for dust, but most feel this not probable. The Romans used the word abacus for any flat table or board, including the top plate in the capital of a Doric column.
Here is a picture of a Chinese Abacus from the excellent web site of Luis Fernandes. Click on the abacus and it will link you to his site where you can learn more about the history and use of the abacus, and even use a java applet of several different types of abaci (The plural of abacus may either be abacuses or abaci. In the second version the "ci" sounds like "sigh").
The word abacus, sometimes with the spelling abbacus, is often used to mean arithmetic or computation in general. In a posting to the Historia-Matematica newsgoup Heinz Lueneburg wrote,
"Concerning the Italian use of the word "abbaco" my Italian-German dictionary of the 19th century says that abbaco means 'elementary reckoning'. ... One finds the word with this meaning in Carlo Collodi, Le avventure di Pinocchio. Lots of editions.
Geppetto enters the room, where Maestro Ciliegia is sitting on the ground, and asks him what he is doing there. "Insegno l'abbaco alle formicole = I teach ciphering to the ants" was the reply.
My 20th century dictionary gives the meaning 'primer to arithmetic' ... ".

The origin of this double meaning seems to trace back to the use by Leonardo Pisano in his Liber Abbaci
Teachers may be interested in this interactive java abbacus . You can adjust to different bases and set the decimal point. You can also choose between Japanese, Korean, Russian and other types.
For those who aspire to advanced skills or historical knowldege on the topic, this link has some nice instrucion.
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