The First Mathematicians
Babylonians: Pythagorean Triples and Problems to Solve
Them
Another Babylonian tablet, dated between 1900 BC and 1600
BC contains certain Pythagorean triples where
a2 + b2 = c2
Many believe that it is the oldest number theory document
ever recorded. Another Babylonian tablet contains the problem
4 is the length and 5 the diagonal. What is the breadth?
Its size is not known. 4 times 4 is 16. 5 times 5 is 25.
You take 16 from 25 and there remains 9. What times shall
I take in order to get 92 3 times 3 is 9. 3 is
the breadth.
This is a good example of using Pythagorean triples to
solve certain problems by the Babylonians.
Egyptians and Romans: Number System
The Roman and Egyptian systems did not make Arithmetic
calculations easy. Multiplication of Roman numerals is nearly
impossible and exceedingly complex. Unlike the Babylonians,
the Egyptians did not develop fully their understanding
of mathematics. Instead, they concerned themselves with
practical applications of mathematics.
Egyptians and Romans: Multiplication
In 1650 BC, the scribe Ahmes wrote the Rhind Papyrus, named
for its Scottish Egyptologist author A. Henry Rhind. The
scroll is 6 meters long and 1/3 of a meter wide. The scribe
Ahmes was copying a document predated 200 years before him.
Consider, for instance, the multiplication of 41 and 59.
41 59
1 59
2 118
4 236
8 472
16 944
32 1888
64 3776
Since 41 falls between 32 and 64, they carry out the following
simple subtraction problem
41 - 32 = 9, 9 - 8 = 1, 1 - 1 = 0
Hence,
41 = 32 + 8 + 1
Then add the corresponding totals
59
1 59 X
2 118
4 236
8 472 X
16 944
32 1888 X
2419
Hence the answer, 2419. If the factors were reversed and
the factors of 41 used, then the same answer could be reached.
These are two good examples of different historical cultures
solving the same types of problems totally differently before
modern mathematics. 1 2
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