Egyptian numerals

The system of ancient Egyptian numerals was used in

The following hieroglyphs were used to denote powers of ten:

Value	1	10	100	1,000	10,000	100,000	1 million, or many
Hieroglyph
Gardiner's sign list ID	Z1	V20	V1	M12	D50	I8	C11
Description	Single stroke	Cattle hobble	Coil of rope	Water lily (also called lotus)	Bent finger	Tadpole	Heh[3]

Multiples of these values were expressed by repeating the symbol as many times as needed. For instance, a stone carving from Karnak shows the number 4,622 as:

Egyptian hieroglyphs could be written in

]

Zero and negative numbers

nfr	heart with trachea beautiful, pleasant, good

By 1740 BCE, the Egyptians had a symbol for zero in accounting texts. The symbol nfr (𓄤), meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line.^[4]

Fractions

Fractions were written with this fractional

${\displaystyle ={\frac {1}{3}}}$

Special symbols were used for 1⁄2 and for the non-unit fractions 2⁄3 and, less frequently, 3⁄4:

${\displaystyle ={\frac {1}{2}}}$

${\displaystyle ={\frac {2}{3}}}$

${\displaystyle ={\frac {3}{4}}}$

If the denominator became too large, the "mouth" was just placed over the beginning of the "denominator":

${\displaystyle ={\frac {1}{100}}}$

Written numbers

As with most modern day languages, the ancient Egyptian language could also write out numerals as words phonetically, just like one can write thirty instead of "30" in English. The word (thirty), for instance, was written as

while the numeral (30) was

This was, however, uncommon for most numbers other than one and two and the signs were used most of the time.^{[citation needed]}

Hieratic numerals

As administrative and accounting texts were written on

Boyer proved 50 years ago^[when?] 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—combining the signs for 9000, 900, 90, and 9—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.^{[citation needed]}

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

Two famous mathematical papyri using hieratic script are the Moscow Mathematical Papyrus and the Rhind Mathematical Papyrus.^{[citation needed]}

Egyptian words for numbers

The following table shows the reconstructed Middle Egyptian forms of the numerals (which are indicated by a preceding asterisk), the

• Egyptian language
• Egyptian mathematics

References

Bibliography

• Allen, James Paul (2000). Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphs. Cambridge: Cambridge University Press. Numerals discussed in §§9.1–9.6.
• Gardiner, Alan Henderson (1957). Egyptian Grammar; Being an Introduction to the Study of Hieroglyphs. 3rd ed. Oxford: Griffith Institute. For numerals, see §§259–266.
• Goedicke, Hans (1988). Old Hieratic Paleography. Baltimore: Halgo, Inc.
• Möller, Georg (1927). Hieratische Paläographie: Die Ägyptische 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)

External links

Wikimedia Commons has media related to Hieroglyphs of Egypt: Numerals.

• Introduction to Hieroglyphs Numbers and Fractions at the Wayback Machine (archived September 29, 2007)
• Numbers and dates at the Wayback Machine (archived March 4, 2001)
• Egyptian Numbers at the Wayback Machine (archived January 12, 2004)
• Egyptian Math History