Homework 2

Reminder: You can (and are encouraged to) discuss problems with your classmates. Then write down the answers by yourself.

1. Write 55667 in the Mayan number system (We will disucss that it was not completely base 20, but you may assume so for this problem)
2. Write 55667 in the Mesopotamian number system.
3. Imagine that you are an Egyptian scribe who only knows to write numbers in the Egyptian hieroglyphic number system. Add 356 and 996. Show your work, paying special attention to regrouping (or “carrying”).
4. Using Ancient Egyptian techniques, multiply 37 by 40.
5. Using Ancient Egyptian techniques,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)
6. Multiply 8 by (2+1/2+1/16) in the Egyptian way
7. 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)?
8. What was the purpose of the Rhind Papyrus ? Read the problems and make a conjecture. Justify 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?

• The following is a paragraph from "The universal history of numbers", by Georges Ifrah, "Another example of high numbers it is from a statue from Hieraconpolis, dating from 2800 BCE, where the number of enemies slain by a king called KhaSeKhem are shown as X by the following sign”. You need to find out the X, that is the number of enemies slain from the hieroglyphic below. Note that the book continues “Early examples show rather irregular outlines and groupings of the signs.” Our example shows such an irregular grouping.

Sample quizz 2

1. Write 55667 in the Mesopotamian number system.
2. Imagine that you are an Egyptian scribe who only knows to write numbers in the Egyptian hieroglyphic number system. Add 356 and 996. Show your work, paying special attention to regrouping (or “carrying”).
3. Using Ancient Egyptian techniques,divide 1935 by 43.
4. Multiply 8 by (2+1/2+1/16) in the Egyptian way
5. What was the purpose of the Rhind Papyrus ? You already read the problems for the homework so you are in position to make a conjecture. Justify 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?