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The system of Egyptian numerals was a numeral system used in ancient Egypt. 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 beautiful Egyptian alphabet.The Egyptian system used bases of ten
Digits and numbersThe following hieroglyphs were used to denote powers of ten:
Egyptian hieroglyphs could be written in both directions (and even vertically). This example is written left-to-right and top-down; on the original stone carving, it is right-to-left, and the signs are thus inverted. FractionsRational numbers could also be expressed, but only as sums of unit fractions, i.e. sums of reciprocals of positive integers, except for 2/3 and 3/4. The hieroglyph indicating a fraction looked like a mouth, which meant "part":
Fractions were written with this fractional solidus, i.e. the numerator 1, and the positive denominator below. Thus, 1/3 was written as:
If the denominator became too large, the "mouth" was just placed over the beginning of the "denominator":
Addition and subtractionFor plus and minus signs, the hieroglyphs
were used: if the feet pointed into the direction of writing, it signified addition, otherwise subtraction. [1] Written numbersBesides this numeral system, the ancient Egyptian language could also write out numbers as words, phonetically, just like one can write "thirty" instead of 30 in English. "Thirty", for instance, was written as
while the number 30 was
This was, however, uncommon for most numbers other than one and two. Hieratic numeralsAs 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 utilise 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 utilise 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—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 Western 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 standardised 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 numbersThe following table shows the reconstructed Middle Egyptian forms of the numerals[2] (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 majiscule letter "A" in some reconstructed forms means that the quality of that vowel remains uncertain:
See alsoReferences
Notes
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