# Berlin Papyrus 6619

Berlin Papyrus 6619, as reproduced in 1900 by Schack-Schackenburg

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.

## 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. 1800BC–1649BC).[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.