- Using Ancient Egyptian techniques, multiply 37 by 40 and divide 1935 by 43. (Note: The division has remainder 0. The Egyptians had a way to deal with non-zero remainders, but we did not discussed this in depth in the lectures)
- Multiply 8 by (2+1/2+1/16) in the Egyptian way
- Explain in your own words how Problem 4 is justified in the Rhind Papyrus. (It is explained in the posted translation, you have to read it, process it, and re-explain it)
- A cylindrical granary of diameter 18 khets and height 10 khets. What is the amount of grain that goes into it? (In other words, compute the volume). Perform the products in the Egyptian way. Compute the area of a circle following the procedure of the Problem 50 of the Rhind Papyrus Express your result in khet^3 (cubic khets).(Of course, this way of expressing the result is not as it was done in Egypt, their measures of volume will not be discussed in this course.)
- Imagine that you are an Egyptian scribe. This time, you are working on the Moscow papyrus. You have to write (in English) the instructions of how to compute the volume of a square pyramid of side length 9 khets and height 9 khets (Note: Your solution should be similar to that of Problem 14 of the Moscow papyrus. And yes, this problem is easy.)
- The Problem 79 of the Rhind papyrus states:. There are seven houses; in each house there are seven cats; each cat kills seven mice; each mouse has eaten seven grains of barley; each grain would have produced seven hekat. What is the sum of all the enumerated things? Do you think this problem has a practical application or it is motivated by curiosity (in other words, it is form of recreational mathematics)?
- What was the purpose of the Rhind Papyrus ? Read the problems and make a conjecture. Justfify your answer in one or two paragraphs. Most scholars think it was like a “book” to study from, in order to be able to resolve pratical problems. Some see evidence that Egyptian mathematics was studied as a pure science. What is your opinion?
- Two websites (website 1 and website 2) contain information of ancient Egyptian mathematics. (You have to scroll down to find Egyptian mathematics in website 2). Do you think the information these websites present is reliable? Why or why not? What do you think of the sentence " It also contains evidence of other mathematical knowledge, including unit fractions, composite and prime numbers”?