Pefsu problem (nonfiction)

Hieroglyph for "grain".

In ancient Egyptian mathematics, a pefsu problem was a mathematical problem involving grain, bread, and beer.

Description

Pefsu is the conventional term for the strength of bread or beer made from a heqat (unit) of grain; it is often translated as "the cooking" or "the cooking ratio (or number)."

A general mathematical expression is:

Pefsu = (no. of loaves of bread, or jugs of beer) / (no. of heqats of grain)

The higher the pefsu number, the weaker the bread or beer.

Example

Problem 8 in the Moscow Mathematical Papyrus translates as:

(1) Example of calculating 100 loaves of bread of pefsu

(2) If someone says to you: “You have 100 loaves of bread of pefsu

(3) to be exchanged for beer of pefsu

(4) like 1/2 1/4 malt-date beer"

(5) First calculate the grain required for the 100 loaves of the bread of pefsu

(6) The result is 5 heqat. Then reckon what you need for a des-jug of beer like the beer called 1/2 1/4 malt-date beer

(7) The result is 1/2 of the heqat measure needed for des-jug of beer made from Upper-Egyptian grain

(8) Calculate 1/2 of 5 heqat, the result will be 2 1/2

(9) Take this 2 1/2 four times

(10) The result is 10. Then you say to him:

(11) Behold! The beer quantity is found to be correct"

Significance

Pefsu was a particularly useful number to know in a barter economy.

In the Rhind papyrus, ten problems deal with pefsu of bread and beer (69-78), eight with the calculation of large areas (48-55), six involve various quantities of grain (35—38, 80-81), six concern the calculation of the volume of rectangular and cylindrical granaries (41-46); then eight focus on the distribution of loaves among men (I-6, 63, 65), one on the distribution of fat (66) and one of grain (68), and three on the distribution of focus to various animals (82-84).

This means that, out of eighty-seven problems contained in this document, thirty deal directly with food production and fourteen with the distribution of food.

In the Moscow papyrus, out of twenty-five problems, ten focus on pefsu of bread and beer, and six on the calculation of areas.

The huge task of re-organizing the land after the annual inundation, the repeated necessity of measuring the fields, the ability to forecast the productivity of the land and to calculate the consequent ‘taxes' and the storage of the products, were all activities that required simple, efficient, and flexible mathematical management.

Conveniently based on a system of intertwined units of measurement, it allowed scribes and technicians to exchange information easily and ensure an equitable distribution of goods.

Nonfiction cross-reference

• Mathematics (nonfiction)

References

"The Algorithmic Structure of the Egyptian Mathematical Problem Texts", in: John Steele and Annette Imhausen (eds.). Under One Sky: Astronomy and Mathematics in the Ancient Near East, Proceedings of the Conference held in the British Museum, London, June 25-27, 2001], (Alter Orient und Altes Testament 297), Munster 2002: 147-166 (Interpretation of Egyptian mathematical problems using their algorithmic features).

External links

• Ancient Egyptian mathematics @ Wikipedia
• Ancient Egyptian multiplication @ Wikipedia
• Egyptian algebra @ Wikipedia
• Moscow Mathematical Papyrus @ Wikipedia
• Ancient Egyptian Science: Ancient Egyptian Mathematics @ books.google.com
• Math Puzzles’ Oldest Ancestors Took Form on Egyptian Papyrus @ New York Times - In the Rhind papyrus, its scribe, known as Ahmes, introduces the roughly 85 problems by saying that he is presenting the "correct method of reckoning, for grasping the meaning of things and knowing everything that is, obscurities and all secrets."
• Egyptian Hieroglyphics Translator @ ipetisut.com