Numbers: Their Tales, Types, and Treasures.

Chapter 3: Numbers in History

 

3.2.NUMBERS IN EGYPT—THE FIRST DECIMAL SYSTEM IN HISTORY

Symbols for writing numbers appeared in Egypt at about the same time as in Mesopotamia, about 3000 BCE. As was the case in Mesopotamia, Egyptian mathematics developed out of practical needs. Mensuration; redistributing land after Nile floods; planning irrigation channels, pyramids, and temples; computing wages and taxes—all these tasks became so complex that human memory and verbal means alone became insufficient, and the need arose to record in written form words, orders, accounts, inventories, censuses, and so on. The Egyptian symbols were called grammata hierogluphika (“carved sacred signs”) by the Greeks, from which the common name “hieroglyphs” is derived. Initially, hieroglyphs were pictograms or ideograms (symbols representing a word or idea) and later evolved into a representation of sounds (consonants). Hieroglyphs were either carved in stone monuments or written on papyrus, a paperlike material made from a grasslike plant (Cyperus papyrus) that grew to a height of three meters in the Nile Delta. In the dry climate of Egypt, papyrus lasts for a long time, and numerous documents have survived until today. We know about Egyptian mathematics essentially from a few papyri with mathematical content, written toward the end of the Middle Kingdom (about 1700 BCE) in hieratic script. The hieratic script consists of symbols that are late forms of hieroglyphs, obtained from them through a process of continuing simplification and schematization. The papyrus Rhind, written by the scribe Ahmose, contains eighty-five mathematical problems. This collection of exercises on geometry and arithmetic probably served to introduce other scribes to the art of mathematics and computation. Other famous papyri devoted to mathematics are the papyrus Moscow and the mathematical leather roll, which is now at the British Museum in London.

The Egyptians used a base-10 system. From the very beginning, they could write very large numbers, with special hieroglyphs for 10, 100, 1000, and so on, up to one million (see figure 3.4).

images

Figure 3.4: Hieroglyphs for powers of 10.

These symbols are for when writing from left to right. The symbols get flipped horizontally if the line containing the numeral is to be read from right to left.

It is very easy to understand how numerals were formed from these basic symbols. The numeral system was not a place-value system, but—very similar to the later Roman numeral system—based on addition. They simply repeated the corresponding symbol as often as needed. For example, the number 2578 would appear as in figure 3.5.

images

Figure 3.5: The number 2578 in hieroglyphs.

The Egyptians had no symbol for zero, and it was not needed to write numbers unambiguously.