history of mathematics - National STEM Centre

24
The Babylonians
which stand in the relation to one another of a number and its reciprocal, to be
understood in the most general sense as numbers whose product is a power of 60.
Obv.
.T'\^V>^
' f . \f~ X '
tf'&S
Figure 2.12
rtpnf^S^
:t=*r-3^- nrtvV.',33^=PTC "
Obverse
/ Jy I tTV"" T' 1 [The igib]um exceeded the
igum by 7.
2 What are [the igum and] the
igibuml
3-5 As for you - halve 7, by which
the igibum exceeded the igum ,
and (the result is) 3;30.
6-7 Multiply together 3;30 with
3 ;30, and (the result is) 12;15.
8 To 12; 15, which resulted for
you,
9 add [ 1 ,0, the produ]ct, and (the
result is) 1,12;15.
10 What is [the square root of
1],12;15? (Answer:) 8;30.
1 1 Lay down [8;30 and] 8;30, its
equal, and then
Reverse
1 -2 subtract 3;30, the takiltum,
from the one,
3 add (it) to the other.
4 One is 12, the other 5.
5 12 is the igibum, 5 the igum.
2 Follow through the instructions in a modern algebraic format.
3 How should you solve the pair of equations
Babylonian scribe?
= 7;30
Geometry in the Old Babylonian period
if you were a
So far you have explored the algebra of the Old Babylonians. Until recently their
contribution to geometry was thought to be much less than is now known to be the
case. In particular, a group of mathematical tablets, which seems to challenge this
assumption, has been found at Susa. In Activity 2.12, you will see an example of
one such tablet.