Egyptian numerals

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Egyptian numerals

The system of Ancient Egyptian numerals was a numeral system used in ancient Egypt aka Kemet. It was a decimal system, often rounded off to the higher power, written in hieroglyphs. The hieratic form of numerals stressed an exact finite series notation, being ciphered one:one onto the Egyptian alphabet.The Ancient Egyptian system used bases of ten.

Digits and numbers

The following hieroglyphs were used to denote powers of ten:Fractions were written with this fractional solidus, "i.e.", the numerator 1, and the positive denominator below. Thus, 1/3 was written as:

For plus and minus signs, the hieroglyphs

This was, however, uncommon for most numbers other than one and two, and also the signs were used a lot in their time.

Hieratic numerals

As most administrative and accounting texts were written on papyrus or ostraca, rather than being carved into hard stone (as were hieroglyphic texts), the vast majority of texts employing the Egyptian numeral system utilize the hieratic script. Instances of numerals written in hieratic can be found as far back as the Early Dynastic Period. The [Old Kingdom] Abusir papyri are a particularly important corpus of texts that utilize hieratic numerals.

Boyer proved 50 years ago that hieratic script used a different numeral system, using individual signs for the numbers 1 to 9, multiples of 10 from 10 to 90, the hundreds from 100 to 900, and the thousands from 1000 to 9000. A large number like 9999 could thus be written with only four signs&mdash;combining the signs for 9000, 900, 90, and 9&mdash;as opposed to 36 hieroglyphs. Boyer saw the new hieratic numerals as ciphered, mapping one number onto one Egyptian letter for the first time in Human history. Greeks adopted the new system, mapping their counting numbers onto two of their alphabets, the Doric and Ionian.

In the oldest hieratic texts the individual numerals were clearly written in a ciphered relationship to the Egyptian alphabet. But during the Old Kingdom a series of standardized writings had developed for sign-groups containing more than one numeral, repeated as Roman numerals practiced. However, repetition of the same numeral for each place-value was not allowed in the hieratic script. As the hieratic writing system developed over time, these sign-groups were further simplified for quick writing; this process continued into Demotic as well.

Two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus.

Egyptian words for numbers

The following table shows the reconstructed Middle Egyptian forms of the numerals [John B. Callender, "Middle Egyptian", 1975] (which are indicated by a preceding asterisk), their transliterated forms in hieroglyphs (indicated between square brackets), and their later Coptic equivalents which give Egyptologists clues as to the vocalism of the original Egyptian numbers. The majuscule letter "A" in some reconstructed forms means that the quality of that vowel remains uncertain:

*Ancient Egypt
*Egyptian language
*Egyptian mathematics

References

*Allen, James Paul. 2000. "Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphs". Cambridge: Cambridge University Press. Numerals discussed in §§9.1&ndash;9.6.
*Gardiner, Alan Henderson. 1957. "Egyptian Grammar; Being an Introduction to the Study of Hieroglyphs". 3rd ed. Oxford: Griffith Institute. For numerals, see §§259&ndash;266.
*Goedicke, Hans. 1988. "Old Hieratic Paleography". Baltimore: Halgo, Inc.
*Möller, Georg. 1927. "Hieratische Paläographie: Die aegyptische Buchschrift in ihrer Entwicklung von der Fünften Dynastie bis zur römischen Kaiserzeit." 3 vols. 2nd ed. Leipzig: J. C. Hinrichs'schen Buchhandlungen. (Reprinted Osnabrück: Otto Zeller Verlag, 1965)

Notes

* [http://www.greatscott.com/hiero/numbers.html Introduction]
* [http://www-history.mcs.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html Egyptian numerals]
* [http://www.egyptvoyager.com/hieroglyph_lesson7.htm Numbers and dates]
*http://egyptianmath.blogspot.com

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