Civilisation reached a high level in Egypt at an early period. The country was well suited for the people, with a fertile land thanks to the river Nile yet with a pleasing climate. It was also a country which was easily defended having few natural neighbours to attack it for the surrounding deserts provided a natural barrier to invading forces. As a consequence Egypt enjoyed long periods of peace when society advanced rapidly. By 3000 BC two earlier nations had joined to form a single Egyptian nation under a single ruler. Agriculture had been developed making heavy use of the regular wet and dry periods of the year. The Nile flooded during the rainy season providing fertile land which complex irrigation systems made fertile for growing crops. Knowing when the rainy season was about to arrive was vital and the study of astronomy developed to provide calendar information. The large area covered by the Egyptian nation required complex administration, a system of taxes, and armies had to be supported. As the society became more complex, records required to be kept, and computations done as the people bartered their goods. A need for counting arose, then writing and numerals were needed to record transactions. By 3000 BC the Egyptians had already developed their hieroglyphic writing (see our article Egyptian numerals for some more details). This marks the beginning of the Old Kingdom period during which the pyramids were built. For example the Great Pyramid at Giza was built around 2650 BC and it is a remarkable feat of engineering. This provides the clearest of indications that the society of that period had reached a high level of achievement. Hieroglyphs for writing and counting gave way to a hieratic script for both writing and numerals. Details of the numerals themselves are given in our article Egyptian numerals. Here we are concerned with the arithmetical methods which they devised to work with these numerals The Egyptian number systems were not well suited for arithmetical calculations. We are still today familiar with Roman numerals and so it is easy to understand that although addition of Roman numerals is quite satisfactory, multiplication and division are essentially impossible. The Egyptian system had similar drawbacks to that of Roman numerals. However, the Egyptians were very practical in their approach to mathematics and their trade required that they could deal in fractions. Trade also required multiplication and division to be possible so they devised remarkable methods to overcome the deficiencies in the number systems with which they had to work. Basically they had to devise methods of multiplication and division which only involved addition. Early hieroglyphic numerals can be found on temples, stone monuments and vases. They give little knowledge about any mathematical calculations which might have been done with the number systems. While these hieroglyphs were being carved in stone there was no need to develop symbols which could be written more quickly. However, once the Egyptians began to use flattened sheets of the dried papyrus reed as "paper" and the tip of a reed as a "pen" there was reason to develop more rapid means of writing. This prompted the development of hieratic writing and numerals. There must have been a large number of papyri, many dealing with mathematics in one form or another, but sadly since the material is rather fragile almost all have perished. It is remarkable that any have survived at all, and that they have is a consequence of the dry climatic conditions in Egypt. Two major mathematical documents survive. You can see an example of Egyptian mathematics written on the Rhind papyrus and another papyrus, the Moscow papyrus, with a translation into hieratic script. It is from these two documents that most of our knowledge of Egyptian mathematics comes and most of the mathematical information in this article is taken from these two ancient documents.
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