Summary
The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear,[1] is one of the primary sources of ancient Egyptian mathematics.[2] One of the two mathematics problems on the Papyrus may suggest that the ancient Egyptians knew the Pythagorean theorem.
| Berlin Papyrus 6619 | |
|---|---|
 Berlin Papyrus 6619, as reproduced in 1900 by Schack-Schackenburg | |
| Created | c. 1800 BC |
| Discovered | Egypt |
| Present location | Berlin, Germany |
Description, dating, and provenance edit
The Berlin Papyrus 6619 is an ancient Egyptian papyrus document from the Middle Kingdom,[3] second half of the 12th (c. 1990–1800 BC) or 13th Dynasty (c. 1800 BC – 1649 BC).[4] The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902.[5][6]
Connection to the Pythagorean theorem edit
The Berlin Papyrus contains two problems, the first stated as "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other."[7] The interest in the question may suggest some knowledge of the Pythagorean theorem, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations x2 + y2 = 100 and x = (3/4)y reduce to the single equation in y: ((3/4)y)2 + y2 = 100, giving the solution y = 8 and x = 6.
See also edit
References edit
- ^ Lumpkin, Beatrice (2004), The Mathematical Legacy of Ancient Egypt - A Response to Robert Palter, National Science Foundation, p. 17, CiteSeerX 10.1.1.372.5877
- ^ "Egyptian Mathematical Papyri - Mathematicians of the African Diaspora", www.math.buffalo.edu
- ^ Rossi, Corinna (2004), Architecture and Mathematics in Ancient Egypt, Cambridge University Press, p. 217
- ^ Clagett, Marshall (1999), Ancient Egyptian Science, vol. 3, American Philosophical Society, p. 249
- ^ Schack-Schackenburg, Hans (1900), "Der Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in German), 38 (1): 135–140, doi:10.1524/zaes.1900.38.jg.135, S2CID 193647129
- ^ Schack-Schackenburg, Hans (1902), "Das kleinere Fragment des Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in German), 40 (1): 65–66, doi:10.1515/zaes-1902-0109, S2CID 193570611
- ^ Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.
External links edit
- Simultaneous equation examples from the Berlin papyrus
- Two algebra problems compared to RMP algebra
- Two suggested solutions