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.
Description, dating, and provenance
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]
Connection to the Pythagorean theorem
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."[6] 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
List of ancient Egyptian papyri
Papyrology
Timeline of mathematics
Egyptian fraction
References
Lumpkin, Beatrice (2004). "The Mathematical Legacy of Ancient Egypt - A Response to Robert Palter". National Science Foundation: 17. CiteSeerX 10.1.1.372.5877.
Williams, Scott, Egyptian Mathematical Papyri, SUNY-Buffalo
Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press 2004, p.217
Marshall Clagett, Ancient Egyptian Science, Vol 3, 1999 [1], p.249.
Schack-Schackenburg, Hans (1900), "Der Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in German), 38: 135–140 (vol. 36-39, pages 506–514),
Schack-Schackenburg, Hans (1902), "Das kleinere Fragment des Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in German), 40: 65–66.
Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.
External links
Simultaneous equation examples from the Berlin papyrus
Two algebra problems compared to RMP algebra
Two suggested solutions
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
