Rhind/Ahmes Mathematical Papyrus

The Rhind/Ahmes mathematical papyrus was transcribed by a scribe named Ahmes between the end of the Egypt’s Middle Kingdom and the genesis of the New Kingdom. As such, it is written in hieratic and claims, among other things, to be a “thorough study of all things, insight into all that exists, knowledge of all obscure secrets.” It contains a collection of 84 exercises geared for students of mathematics. Included are exercises in arithmetic, notations, fractions, algebra, geometry, and mensuration. An example of one of the problems included is: “In seven houses there are seven cats. Each cat catches seven mice. Each mouse would have eaten seven ears of corn and each ear of corn, if sown, would have produced seven gallons of grain. How many

things are mentioned in total?”
The Greeks admired Egyptian mathematical knowledge, and while the Rhind papyrus does not contain very complex problems, it is not only one of the few surviving artifacts that gives us an example how ancient Egyptians deciphered numbers, it is also, to date, the best example we have.

While papyrus is relatively inexpensive to produce, this roll, measuring 17 feet, would have cost what was equivalent to the price of a goat.

Therefore, it would have been too expensive to own for most people, but if one were ambitious and wanted a role within the Egyptian state, it would be a valuable document to possess. In an earlier papyrus, the Lansing papyrus, the scribe wrote for his pupils “See, I am instructing you ... so that you may become one who is trusted by the king, so that you may open treasuries and granaries, so that you may take delivery from the corn-bearing ship at the entrance to the granary, so that on feast days you may measure out the god’s

offerings.”

The running of a society as complex as ancient Egypt would have required the skills of people who could oversee the creation of their buildings, manage food stock, plan military strategies, compute the yearly flood levels of the Nile, and organize payments and debts. To be in the employed in the service of the Pharaohs, one needed to possess a certain competency of mathematics and writing, and this is why the Rhind would have been a valuable teaching and learning tool to own for anyone who had the ambition to work for the Court.

The calculations are geared to be useful in solving practical problems encountered in their daily lives. Things like the amount of food one needed to feed livestock, how to calculate pyramid slopes, etc. It was intended to be a primer for people desiring employment with the state as is evident from its contents and detailed title: “The correct method of reckoning, for grasping the meaning of things, and knowing everything - obscurities and all secrets.”

Other calculations in the papyrus dealt with things such as how many gallons of beer or loaves of bread could you get from a given amount of grain, along with how to determine whether or not what you have been paying for has been undiluted.

It also tells you how to calculate how much to feed your free range geese as opposed to ones kept in a coop. According to one of the problems, one gave less grain to the captive geese as they did not have the opportunity to move much; so they would be cheaper to fatten up for the market, ergo, more profitable. Obviously, animal rights activists were not plentiful in ancient

Egypt.
Problem 72 deals with another domestic problem that was commonplace in Egypt. How many loaves of "strength" 45 are equivalent to 100 loaves of strength 10? A “strength is to 100 grain density, so it is mathematically written thus:
Strength = _____1_____
Grain Density
Now, using the ancient rule of three (the rule to determine the fourth and unknown quantity in the expression a/b = c/d in which the other three are known), we must solve the problem: