Berlin Papyrus 6619

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Berlin Papyrus 6619
Papyrus Berlin 6619.jpg
Berlin Papyrus 6619, as reproduced in 1900 by Schack-Schackenburg
Createdc. 1800 BC
Discovered Egypt
Present location Berlin, Germany

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.

Contents

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] It is written in the hieratic script. [5] The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902. [6] [7]

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." [8] 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

References

  1. 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
  2. "Egyptian Mathematical Papyri - Mathematicians of the African Diaspora", www.math.buffalo.edu
  3. Rossi, Corinna (2004), Architecture and Mathematics in Ancient Egypt, Cambridge University Press, p. 217
  4. Clagett, Marshall (1999), Ancient Egyptian Science, vol. 3, American Philosophical Society, p. 249
  5. Gillings, Richard (1972). "Hieroglyphic and Hieratic Writing and Numbers". Mathematics in the Time of the Pharaohs (PDF). New York: Dover Publications, Inc. pp. 4–10. ISBN   978-0486243153 . Retrieved 3 June 2025.
  6. 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
  7. 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
  8. Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.