Ancient Mathematical Concepts

The questions below should be answered completely. Essay question answers should be typed.

Problems

In the readings for this chapter, focus on the following questions.

1. Give an analysis of the ordinal vs. cardinal theories of the origin of counting (or sense of numbers)
2. Conjecture as to why notches (in groups of five) may have been carved into the wolf bone found in Czeckoslovakia. Why was a bone used? Why not wood or animal skin?
3. The Vedda tribesmen knew the concept of one-to-one correspondence but had no words for numbers? Give an argument for the impossibility of this?
4. In tribal setting counting seems to have a number of uses. Calculation is another story. Conjecture several requirements for calculations such as addition and subtraction. That is, in a tribal setting what sorts of activities or needs actually require additive or subtractive calculations? How about multiplication or division? Are there any conceivable applications of geometry in the tribal setting?
5. At what level of societal growth do geometry and mensuration become essentials?
6. What "number-words" do we still use today?

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