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# Berlin Papyrus 6619

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### Berlin Papyrus 6619

The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear,[1] is an ancient Egyptian papyrus document from the Middle Kingdom,[2] second half of the 12th or 13th dynasty.[3] The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902.[4]

The papyrus is one of the primary sources of ancient Egyptian mathematics.[5]

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. ^ , 2004. National Science Foundation. p17The Mathematical Legacy of Ancient Egypt - A Response to Robert PalterLumpkin, Beatrice,
2. ^ Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press 2004, p.217
3. ^ Marshall Clagett, Ancient Egyptian Science, Vol 3, 1999 [1], p.249.
4. ^ Schack-Schackenburg, Hans (1900), "Der Berliner Papyrus 6619", Zeitschrift für ägyptische Sprache und Altertumskunde (in Deutsch) 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 Deutsch) 40: 65–66.
5. ^ Williams, Scott, Egyptian Mathematical Papyri, SUNY-Buffalo
6. ^ Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.