Transcript ‘Abaci’

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)
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 BC)
The number 73 would be written like this:
1 lot of 60 plus 13
Ancient Egyptian
Ancient Egyptians used disks of different sizes as counters.
It is unclear whether these were used on a frame
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
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
The Romans invented a portable abacus for engineers and
merchants. It is based on the decimal system.
Roman
This is a representation of a Roman abacus.
When you get to
5 move
this
one
Continue
like
this
andyou
putget
the
other
until
to
These
two
Then
move
these
four
beads
back.are for
100
then
move
columns
Moving
the
beads
again to show the
one
of
these.
fractions.
in
this
column
numbers
from 6
represents
to 9. the
numbers 1 to 4.
When you get to
This column
10 move
one of
represents
these.
millions.
Chinese
The Chinese used abaci in the 2nd Century BC. An abacus
was known as a suànpán which means ‘counting tray’.
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
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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