history of mathematics - National STEM Centre

The Babylonians
Activity 2.7 Square roots
Activity 2.8
Figure 2.9
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Figure 2.8a Figure 2.8b
1 Decipher the numbers on the tablet (Figure 2.8b).
2 What do these numbers mean?
3 How is the number under the diagonal related to the one above?
4 At one point the number under the diagonal is damaged. What symbol is
missing?
But what was the student doing? The number on the diagonal is the length of the
diagonal of a square of side 1 unit. The given square is of side -j unit, so the number
underneath the diagonal is the result of multiplying the diagonal by ^ to obtain the
diagonal of a square of side -j. In fact, it is a scaling operation.
Square roots again
You may wonder how the Babylonians knew that the length of the diagonal is V^.
They could have found this either by geometrical study, or by applying the result
which was later to be called Pythagoras's theorem, which they probably knew,
though not by that name!
1 Deduce from Figure 2.9, without using Pythagoras's theorem, that the length of
the diagonal of the square is V2 .
It is possible that Pythagoras later arrived at his theorem by considering this kind of
diagram.
2 Use Figure 2.9 to prove Pythagoras's theorem in an isosceles right-angled
triangle.
3 The diagram in Figure 2.10 is based on a Chinese text from between 1100 and
600 BC. Prove Pythagoras's theorem from this diagram.