Problem 4
- Write 346 in the traditional Chinese number system,
- 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)
- Write 55667 in the Mesopotamian number system.
- 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… by the following sign”. You need to find out the …, that is the number of enemies slain from the hieroglyphic on the right. Note that the book continues “Early examples show rather irregular outlines and groupings of the signs.” Our example shows such an irregular grouping.
- What is the maximum number of times a numeral can appear en each of the following number systems: Egyptian hieroglyphic, traditional Chinese, Mayan, Mesopotamian and Hindu Arabic. If there is not maximum times, explain why.
- 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”).
- Imagine why and how the positional number system develop. (You do not have to discuss any particular society). There is no “correct” answer to this question.
Sample quiz (4 of the problems below)
- Write 346 in the traditional Chinese number system,
- 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)
- Write 55667 in the Mesopotamian number system.
- Write 5556 in the Egyptian number system.
- 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
Note: Numerals and their values will be given in the quiz.