Moscow Mathematical Papyrus

The Papyrus Moscow 4676 (also Moscow Mathematical Papyrus papyrus or Moscow) is an ancient Egyptian papyrus with mathematical content that contains a collection of 25 math problems. He is 5.44 m long and 8 cm wide, is constructed around the year 1850 BC dated and is next to the Papyrus Rhind one of the most important historical sources for the ancient Egyptian mathematics. He is of the papyri now located in Moscow, the most well-known and therefore got the name.

Discovery history

This papyrus was in 1893 purchased by the Egyptologist Vladimir Semenovich Golenishtchev in Egypt and is originally from Dra Abu el- Naga at Thebes .. The Russian Egyptologist undertook a total of 60 Travel Egypt, on which he himself was not performed by its own excavations, and sold in 1911 his collected Antiques, including the Papyrus Moscow 's Pushkin Museum of Fine Arts in Moscow, where it is still located with the inventory number 4676.

Content

The papyrus is written in hieratic script, whose translation was published in 1930 by Vasily Vasilievich Struve and Boris Alexandrovich Turajew.

The papyrus contains 25 mathematical tasks that are not arranged systematically, such as the Rhind papyrus. Therefore sees Gabriele Höber Camel Papyrus Moscow as a kind of " examination paper " and supports this hypothesis on the one hand with the - compared to other mathematical papyri - relatively small number of tasks and the other by the existing additional remark behind the tasks that roughly translates as follows: " you've really found out. "

The computational tasks include mostly problems with one unknown, the Hau -bill called.

Task 6

Task 6 raises the question of the sides of a rectangle with a given surface (12) and a given aspect ratio ( 3/4). The solution requires the determination of an integer square root ..

Task 10

This task deals with the calculation of a basket surface. Because of gaps in the text and the ambiguity of the symbol for "basket", the exact interpretation is controversial. In the literature can be found, among other interpretations as a surface of a hemisphere, a half-cylinder or a basket-like storage container. Regardless of the exact interpretation, the task but in any case one of the oldest written records of the approximate computation of a curvilinear surface represents the description given below is based on an interpretation as a hemisphere.

From the original text of this task, the following calculation formula, the size d is the aperture Messes of the basket and thus the diameter of the hemispherical bottom circle results:

In comparison, according to current knowledge, the correct formula for the calculation of a hemispherical surface:

That is, the formula corresponds to a use of the following approximate value for the mathematical constant π (Pi):

Task 14

Famous is the task 14, in which the volume of a square pyramid frustum is determined. The formula used is correct and is in modern notation:

When a and b are the page length of the square base and top, and h is the height. In the task becomes concrete with the numbers a = 4, b = 2 and h = 6 expected:

This results in a volume of 56