Moscow Mathematical Papyrus

The Moscow Mathematical Papyrus, also named the Golenishchev Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus with many problems in arithmetic, geometry, and algebra. Golenishchev bought the papyrus in 1892 or 1893 in Thebes. It is now in the Pushkin State Museum of Fine Arts in Moscow, where it stays today.

Based on the writing style of the hieratic text, experts think it was written in the 13th Dynasty and uses ideas from around the 12th Dynasty of Egypt, about 1850 BC. It is about 5.5 m (18 ft) long and between 3.8 and 7.6 cm (1.5 and 3 in) wide. In 1930, a Soviet Orientalist named Vasily Struve split it into 25 problems with answers.

It is a famous old math book, often talked about with the Rhind Mathematical Papyrus. The Moscow Mathematical Papyrus is older, but the Rhind Mathematical Papyrus is bigger.

Exercises contained in the Moscow Papyrus

The Moscow Papyrus has many fun math problems. They are not in any special order. One big topic is geometry, which is about shapes. For example, it shows how to find the surface area of a rounded dome and the space inside a cut-off pyramid.

Other problems include figuring out the length of parts of a ship, solving puzzles to find a missing number, and calculating how strong bread or beer is from the grain used. There are also questions about how much work different jobs might do, like turning logs into smaller sizes or making shoes. The papyrus shows us the cool math skills of ancient Egypt.

Main article: Rhind Mathematical Papyrus

Two geometry problems

The Moscow Mathematical Papyrus has two fun geometry problems.

Problem 10 asks for the surface area of a hemisphere. The ancient Egyptians showed a simple way to find this area. They used easy math and a special number to stand in for π.

Problem 14 asks for the volume of a frustum. A frustum is a pyramid with the top part cut off. The papyrus shows how to calculate this volume using the lengths of the top and bottom squares and the height of the frustum.

Summary

The Moscow Mathematical Papyrus is an old book with math problems. It shows how people in ancient Egypt used special symbols for fractions. For example, they would put a line over the number 4 to mean one-fourth. This book helps us learn about math from a long time ago.

The contents of The Moscow Mathematical Papyrus

No.	Detail
1	Damaged and unreadable.
2	Damaged and unreadable.
3	A cedar mast. 3 ¯ 5 ¯ {\displaystyle {\bar {3}}\;{\bar {5}}} of 30 = 16 {\displaystyle 30=16} . Unclear.
4	Area of a triangle. 2 ¯ {\displaystyle {\bar {2}}} of 4 × 10 = 20 {\displaystyle 4\times 10=20} .
5	Pesus of loaves and bread. Same as No. 8.
6	Rectangle, area = 12 , b = 2 ¯ 4 ¯ l {\displaystyle =12,b={\bar {2}}\;{\bar {4}}l} . Find l {\displaystyle l} and b {\displaystyle b} .
7	Triangle, area = 20 , h = 2 2 ¯ b {\displaystyle =20,h=2\;{\bar {2}}b} . Find h {\displaystyle h} and b {\displaystyle b} .
8	Pesus of loaves and bread.
9	Pesus of loaves and bread.
10	Area of curved surface of a hemisphere (or cylinder).
11	Loaves and basket. Unclear.
12	Pesu of beer. Unclear.
13	Pesus of loaves and beer. Same as No. 9.
14	Volume of a truncated pyramid. V = ( h / 3 ) ( a 2 + a b + b 2 ) {\displaystyle V=(h/3)(a^{2}+ab+b^{2})} .
15	Pesu of beer.
16	Pesu of beer. Similar to No. 15.
17	Triangle, area = 20 , b = ( 3 ¯ 15 ¯ ) h {\displaystyle =20,b=({\bar {3}}\;{\bar {15}})h} . Find h {\displaystyle h} and b {\displaystyle b} .
18	Measuring cloth in cubits and palms. Unclear.
19	Solve the equation 1 2 ¯ x + 4 = 10 {\displaystyle 1\;{\bar {2}}x+4=10} . Clear.
20	Pesu of 1000 loaves. Horus-eye fractions.
21	Mixing of sacrificial bread.
22	Pesus of loaves and beer. Exchange.
23	Computing the work of a cobbler. Unclear. Peet says very difficult.
24	Exchange of loaves and beer.
25	Solve the equation 2 x + x = 9 {\displaystyle 2x+x=9} . Elementary and clear.

Other papyri

Other mathematical texts from Ancient Egypt include the Berlin Papyrus 6619, Egyptian Mathematical Leather Roll, Lahun Mathematical Papyri, and the Rhind Mathematical Papyrus. There are also general papyri such as the Papyrus Harris I and the Rollin Papyrus. For tables showing fractions, you can look at the RMP 2/n table.