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The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is one of the primary sources of
Simultaneous equation examples from the Berlin papyrus
Egyptian mathematics Egyptian papyri {{papyrus-stub
The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is one of the primary sources of ancient Egyptian mathematics
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. , from the Old Kingdom of Egypt
In ancient Egyptian history, the Old Kingdom is the period spanning c. 2700–2200 BC. It is also known ...
. One of the two mathematics problems on the Papyrus may suggest that the ancient Egyptians knew the Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposit ...
.
Description, dating, and provenance
The Berlin Papyrus 6619 is an ancient Egyptian papyrus document from the Middle Kingdom, second half of the 12th (c. 1990–1800 BC) or13th Dynasty
In music or music theory, a thirteenth is the note thirteen scale degrees from the root of a chord and also the interval between the root and the thirteenth. The interval can be also described as a compound sixth, spanning an octave p ...
(c. 1800 BC – 1649 BC). The two readable fragments were published by Hans Schack-Schackenburg in 1900 and 1902.
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."Richard J. Gillings, ''Mathematics in the Time of the Pharaohs'', Dover, New York, 1982, 161. The interest in the question may suggest some knowledge of thePythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposit ...
, though the papyrus only shows a straightforward solution to a single second degree equation in one unknown. In modern terms, the simultaneous equations and reduce to the single equation in ''y'': , giving the solution ''y'' = 8 and ''x'' = 6.
See also
*List of ancient Egyptian papyri
This list of ancient Egyptian papyri includes some of the better known individual papyri written in hieroglyphs, hieratic, demotic or in Greek. Excluded are papyri found abroad or containing Biblical texts which are listed in separate lists.
...
* Papyrology
Papyrology is the study of manuscripts of ancient literature, correspondence, legal archives, etc., preserved on portable media from antiquity, the most common form of which is papyrus, the principal writing material in the ancient civilizations ...
* Timeline of mathematics
* Egyptian fraction
An Egyptian fraction is a finite sum of distinct unit fractions, such as
\frac+\frac+\frac.
That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from ea ...
References
External links
Simultaneous equation examples from the Berlin papyrus
Egyptian mathematics Egyptian papyri {{papyrus-stub