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Berlin Papyrus 6619

## 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, as reproduced in 1900 by Schack-Schackenburg

## 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.

## References

1. ^ Lumpkin, Beatrice (2004). "The Mathematical Legacy of Ancient Egypt - A Response to Robert Palter". National Science Foundation: 17. CiteSeerX 10.1.1.372.5877. `{{cite journal}}`: Cite journal requires `|journal=` (help)
2. ^ Williams, Scott, Egyptian Mathematical Papyri, SUNY-Buffalo
3. ^ Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press 2004, p.217
4. ^ Marshall Clagett, Ancient Egyptian Science, Vol 3, 1999 [1], p.249.
5. ^ Schack-Schackenburg, Hans (1900), "Der Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in German), 38: 135–140, doi:10.1524/zaes.1900.38.jg.135, S2CID 193647129 (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, doi:10.1515/zaes-1902-0109, S2CID 193570611.
6. ^ Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.