History OF Mathematics In Egypt
The ancient Egyptians were possibly the first civilization to practice the
scientific arts. Indeed, the word chemistry is derived from the word
Alchemy which is the ancient name for Egypt.
Where the Egyptians really excelled was in medicine and applied
mathematics. But although there is a large body pf papyrus literature
describing their achievements in medicine, there are no records of how
they reached their mathematical conclusions. Of course they must have
had advanced understanding of the subject because their exploits in
engineering, astronomy and administration would not have been possible
without it.
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The Egyptians had a decimal system using seven different symbols.
1 is shown by a single stroke
10 is shown by a drawing of a hobble for cattle
100 is represented by a coil of rope
1,000 is drawing of a lotus plant
10,000 is represented by a finger
100,000 is represented by a tadpole or frog
1,000,000 is the figure of a god with arms raised above his head
The conventions for reading and writing numbers is quite simple; the
higher number is always written in front of the lower number and where
there is more than one row of numbers, the reader should start at the top.
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You can now an example of Egyptian mathematics: The Rhind papyrus
The Rhind papyrus is named after the Scottish Egyptologist A Henry
Rhind, who purchased it in Luxor in 1858. The papyrus, a scroll about 6
metres long and 1/3 of a metre wide, was written around 1650BC by the
scribe Ahmes who is copying a document which is 200 years older. This
makes the original papyrus and the Moscow papyrus both date from
about 1850BC.
Unlike the Greeks who thought abstractly about mathematical ideas, the
Egyptians were only concerned with practical arithmetic. In fact the
Egyptians probably did not think of numbers as abstract quantities but
always thought of a specific collection of 8 objects when 8 was
mentioned. To overcome the deficiencies of their system of numerals, the
Egyptians devised cunning ways round the fact that their numbers were
suitable for multiplication as shown in the Rhind papyrus which date
from about 1700BC.
The Rhind papyrus recommends that multiplication be done in the
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following way. Assume that we want to multiply 41 by 59. Take 59 and
add it to itself, then add the answer to itself and continue.
41
59
___________________
1
59
2
118
4
236
8
472
16
944
32
1888
___________________
Since 64>41, there is no need to go beyond the 32 entry. Now go through
a number of subtractions
41-32=9, 9-8=1, 1-1=0
to see that 41=32+8+1. Next check the numbers in the right hand column
corresponding to 32, 8, 1 and add them.
59
__________________
1
59
X
2
118
4
236
8
472
X
16
944
32
1888 X
__________________
2419
Notice that the multiplication is achieved with only additions, notice also
that this a very early use of binary arithmetic. Reversing the factors we
have
59
41
__________________
1
41
X
2
82
X
4
164
8
328
X
16
656
X
11
32
1312
___________________
2419
X
You can now see a picture of another papyrus: The Moscow papyrus
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