[Today’s class: More number systems in various (early) civilizations, mainly via worksheets, and including basic arithmetic (Egyptian, Mesopotamian, Chinese, Maya, Aztec, Inca quipu, Roman),
different types of number systems (positional, multiplicative grouping, simple grouping),
learning to use an abacus]
Mathematics 115
Homework Assignment #2
Due Wednesday, January 9, 2002
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Prof. Beery's office hours this week: Tuesday 1/8 11:30 a.m.-12:30 p.m., 4-5 p.m.
Wednesday 1/9 10:30 a.m.-12:30 p.m., 4-5 p.m.
Thursday 1/10 10:30 a.m.-12:30 p.m., 4-5 p.m.
Friday 1/11 1:30 - 3:30 p.m.
and by appointment, Hentschke 203D, x3118
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Read: "Oneness, Twoness, Threeness: How Ancient Accountants Invented Numbers"
"Indian Rope Tricks: A Number of Knotty Problems"
"The King Was in His Counting House . . ."
Do: Answer the following questions about the "Oneness, Twoness, Threeness" essay.
1. Why is the essay titled "Oneness, Twoness, Threeness" (rather than, say, "One,
Two, Three")? Be sure to distinguish between concrete counting and abstract
numbers in your answer.
2. The author of the essay claims that plain clay tokens led to the development of
abstract numbers and that complex clay tokens led to the development of phonetic
writing. Review for me her argument in each case. That is, explain in your own
words (a) how plain clay tokens led to the development of abstract numbers and
(b) how complex clay tokens led to the development of phonetic writing.
3. What's the difference between a "syllabary" and an "alphabet"?
Answer the following two questions about the "Rope Tricks" and "Counting House"
essays.
4. Did everyone in the Persian and Incan societies know how to use the counting
board and record the results? If not, who did?
5. Fill in the blanks: The main difference between the Persian and Incan calculators
was that the Persian calculators recorded their results _____, whereas the Incan
calculators recorded their results _____.
6. Complete the exercises numbered 0 through 4 from "The Abacus" handout.
Wednesday's quiz (20 points) will cover your work from class Monday and the
reading and problems from Homework Assignment #1.