A toy car has a scale factor of 1/40. The diameter of the toy car’s tire is 5/8 inches. What is the diameter of the actual car’s tire?
1. In the Rhind papyrus, the concept of π is described by:
Take a field of diameter 9; take 1/9 th of the diameter. Square the remainder to find the area.
What value does this give for π ?
2. Use the assumed Babylonian square root algorithm of the notes to show that the square root of 3 is approximately 1;45 by beginning with the value 2. Find a three-sexagesimal-place approximation to the reciprocal of 1;45 and use it to calculate a three-sexagesimal-place approximation to the square root of 3.
3. *Explain in several paragraphs the fundamental differences in the mathematics of the Egyptians and the Babylonians and the possible reasons for the differences.
Select a project that is meaningful to you. The project should be a situation for which math is used to help you make a decision or reach a conclusion. Identify the steps you have followed to complete your project. Especially, set up the processes that you use in the form of a formula or equation. Include an introduction that explains in detail what you intend to do.
Section 1: Explain the problem, including assumptions you made at the beginning. The problem should include an analysis of data. Add a table if appropriate. Identify the steps you will follow and indicate where the math is along the way.
Section 2: Identify the methods you use to solve the problem. Explain the processes (formulas) you use to find the solution. Set up a general formula / equation that would be applicable to similar situations.
Section 3: Analyze your findings. An assessment of the solution should include a discussion of the appropriateness of the solution.
Section 4: Include a concluding statement to discuss how the process permitted you to make a decision and what that decision was.
Some possible topics might be:
Ø Designing a home repair project
Ø Planning a trip
Ø Buying a house, a co-op, a car
Ø Planning an important event such as a family reunion or special dinner
Ø Making and tracking an investment in the stock market