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Traditional systems of measurement often had strange rules. An extreme example of this is a problem about a trench found in an old Babylonian...
5. Traditional systems of measurement often had strange rules. An extreme example of this is a problem about a trench found in an old Babylonian tablet. It says that the trench has area 7.5 SAR (we write the numbers in modern notation, rather than in the Babylonian style) and volume 45 SAR, and that the depth is equal to one seventh of the difference between the length and the width. The solution given in the tablet is that the length is 5 GAR and the width is 1.5 GAR. Two things seem strange. First, the text seems to use "SAR" both as a unit of area and as a unit of volume. How can that be? Second, do the numbers work out? Is it true that "the depth is equal to one seventh of the difference between the length and the width"? If not, can you formulate a conjecture about what might be going on?
