Abaci or abacuses
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Abaci (or Abacuses). a brief history. Mesopotamian (2700-2300 BC). There is evidence that abaci were used here for addition and subtraction. Mesopotamian (2700-2300 BC). Historic map. Today. Mesopotamian (2700-2300 BC).

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Abaci (or Abacuses)

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Abaci or abacuses

Abaci (or Abacuses)

a brief history


Mesopotamian 2700 2300 bc

Mesopotamian (2700-2300 BC)

There is evidence that abaci were used here for addition and subtraction.


Mesopotamian 2700 2300 bc1

Mesopotamian (2700-2300 BC)

Historic map

Today


Mesopotamian 2700 2300 bc2

Mesopotamian (2700-2300 BC)

The abaci were a table of successive columns with each column representing an order of magnitude higher than the next (a bit like our number system). Rather than using decimal (base 10), like we use, they used sexagesimal (base 60).


Mesopotamian 2700 2300 bc3

Mesopotamian (2700-2300 BC)

The number 73 would be written like this:

1 lot of 60 plus 13


Ancient egyptian

Ancient Egyptian

Ancient Egyptians used disks of different sizes as counters. It is unclear whether these were used on a frame


Ancient egyptian1

Ancient Egyptian

Herodotus

5th Century BC

Greek Historian

“The Father of History”

He wrote about the Egyptian abaci and compared them to the Greek abaci. They worked in opposite directions.


Grecian

Grecian

They have been using abaci in Greece since 5th century BC.

The oldest abacus discovered so far was Greek and dates back to 300 BC. It is made of slabs of white marble.


Roman

Roman

The Romans invented a portable abacus for engineers and merchants. It is based on the decimal system.


Roman1

Roman

This is a representation of a Roman abacus.

When you get to 10 move one of these.

When you get to 5 move this one and put the other four beads back.

This column represents millions.

Continue like this until you get to 100 then move one of these.

These two columns are for fractions.

Then move these again to show the numbers from 6 to 9.

Moving the beads in this column represents the numbers 1 to 4.


Chinese

Chinese

The Chinese used abaci in the 2nd Century BC. An abacus was known as a suànpán which means ‘counting tray’.


Chinese1

Chinese

The arrangement is similar to Roman abaci but has extra beads so that both decimal and hexadecimal (base 16) numbers could be used.

Techniques had been developed to use the abaci for addition, subtraction, multiplication, division, square roots and cube roots.

This abacus shows the number 6,302,715,408


More modern abaci

More Modern Abaci

The use of abaci spread across the Asia.

In 5th Century AD Indian clerks were using the term shunya (zero) to indicate empty columns on an abacus.

The Japanese started using abaci in 1600 (based on the Chinese one) called a soroban. Even today, pupils in Japanese primary schools are taught to use abaci to aid mental arithmetic.

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