How Egyptian numbers work
Egyptian numerals are a base-10 additive system: there is no positional value and no zero. To write a number, you simply repeat the appropriate hieroglyphs the required number of times, up to nine of each. Order does not mathematically matter, though Egyptians typically wrote larger values first, reading in the direction the signs face.
| Number | Hieroglyphs |
|---|---|
| 3 | πΊπΊπΊ |
| 10 | π |
| 21 | πππΊ |
| 100 | π’ |
| 276 | π’π’ππππππππΊπΊπΊπΊπΊπΊ |
| 1,000 | πΌ |
| 2,026 | πΌπΌπππΊπΊπΊπΊπΊπΊ |
| 4,622 | πΌπΌπΌπΌπ’π’π’π’π’π’πππΊπΊ |
| 10,000 | π |
| 100,000 | π |
Egyptian arithmetic
Addition meant pooling symbols and swapping ten of a kind for the next symbol up. Multiplication used doubling: to multiply 13 by 12, a scribe doubled 12 to get 24, 48 and 96, then added the rows for 1, 4 and 8 (which sum to 13): 12 + 48 + 96 = 156. Fractions were written as sums of unit fractions such as 1/2 + 1/4, with a special sign for 2/3.
History
The Egyptian numeral system dates from around 3100 BC and is one of humanity's earliest written numeral systems, appearing on the Narmer Macehead, which records captured cattle and prisoners in the hundreds of thousands. Ancient Egyptians used it for tax records, grain stores, architectural measurements and census counts. The Rhind Mathematical Papyrus (about 1550 BC) preserves 84 worked problems on fractions, areas and volumes, including an approximation of pi of about 3.16. Scribes writing quickly on papyrus used the simpler hieratic script, which had separate signs for each digit.