[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]

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**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.

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**Wednesday's quiz** (20
points) will cover your work from class Monday and the

reading and problems from Homework Assignment #1.