Abacus
0Abacus, by Wikipedia https://en.wikipedia.org/wiki?curid=655 / CC BY SA 3.0
#Abacus
#Mathematical_tools
#Chinese_mathematics
#Egyptian_mathematics
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Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503.
The woodcut shows Arithmetica instructing an algorist and an abacist （inaccurately represented as Boethius and Pythagoras）.
There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.
The abacus （plural abaci or abacuses）, also called a counting frame, is a calculating tool which has been used since ancient times.
It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Arabic numeral system.
The exact origin of the abacus has not yet emerged.
It consists of rows of movable beads, or similar objects, strung on a wire.
They represent digits.
One of the two numbers is set up, and the beads are manipulated to perform an operation such as addition, or even a square or cubic root.
In their earliest designs, the rows of beads could be loose on a flat surface or sliding in grooves.
Later the beads were made to slide on rods and built into a frame, allowing faster manipulation.
Abacuses are still made, often as a bamboo frame with beads sliding on wires.
In the ancient world, particularly before the introduction of positional notation, abacuses were a practical calculating tool.
The abacus is still used to teach the fundamentals of mathematics to some children, e.
g.
, in post-Soviet states.
Designs such as the Japanese soroban have been used for practical calculations of up to multi-digit numbers.
Any particular abacus design supports multiple methods to perform calculations, including the four basic operations and square and cube roots.
Some of these methods work with non-natural numbers （numbers such as 1.5 and 3⁄4）.
Although calculators and computers are c...
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