# Berlin Papyrus 6619

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 provides evidence that the ancient Egyptians knew the Pythagorean theorem.

## Contents

## Description, dating, and provenanceEdit

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. 1800BC–1649BC).^{[4]} The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902.^{[5]}

## Connection to the Pythagorean theoremEdit

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 *x*^{2} + *y*^{2} = 100 and *x* = (3/4)*y* reduce to the single equation in *y*: ((3/4)*y*)^{2} + *y*^{2} = 100, giving the solution *y* = 8 and *x* = 6.

## See alsoEdit

## ReferencesEdit

**^**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.