Ancient maths index
Centuries-old homework
Depth on the Nile
Building pyramids and preserving bodies weren't the only marks of their civilisation. There was a unique Egyptian system of counting.
Ziggurats and zodiacs
Related programme
Like the Egyptian texts, the mathematical tablets from the Old Babylonian period fall broadly into two categories, table texts and problem texts. Several hundred table texts, tablets consisting solely of tables of numbers, have been found, and many types of calculations appear to have been carried using them. There are tables of squares, multiplication tables, tables of reciprocals (used for division), tables of square and cube roots, combined tables where several of these are present, tables for working out compound interest, tables of weights and measures, and others. Numerical tables seem to have been a staple constituent of Babylonian life, as ubiquitous for them as is the pocket calculator for us today.
Problem texts, by contrast, are rarer, only a hundred or so tablets featuring these have been found and they seem to relate to an educational context or advanced scribal training. Some merely give the problem and the answer; others are more forthcoming on what to do to reach the answer. They are generally written in the context of everyday life and activities, such as weighing and measuring, paying wages, and digging ditches; although they rarely appear to be using real-world examples. Typical examples involve the flooding of a field to a depth of one finger for irrigation, and finding the length of a broken reed used for measuring a field!
Almost invariably the central purpose of a Babylonian problem is the computation of a specific number. The solution is then generally given through a series of instructions. Often these instructions include a step, such as calculating a square root, which is sufficiently difficult to imply the off-stage use of a table text. Many of the problems involve linear and quadratic equations, and there are even some involving cubic and biquadratic equations. There are also problems involving geometrical constructions but these too require the computation of a number, such as the length of a side, or an area, or a volume. Some problems even include diagrams of basic shapes such as triangles, squares and circles. Although all the problems are formulated using specific numbers, it is evident from the methods used to solve them that the Babylonians were in possession of some general rules.
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