1. Do the paper ball experiment using a light weight paper. Record the dimension.
2. Do the paper ball experiment using a medium weight paper. Record the dimension.
3. Do the paper ball experiment using a heavy weight paper. Record the dimension.
4. Do the paper ball experiment using a medium weight paper, but crumple and recrumple the paper balls several times before recording the diameters. Record the dimension.
5. Compare the dimensions obtained in exercises 1 - 4. Explain the differences. Is it possible to get a dimension greater than 3 or less than 2? Explain. Answer
6. With a very sharp serrated knife bisect a paper ball with mass 1. Take care to minimize the compression or distortion of the paper ball while slicing it. What do the revealed edges illustrate? Estimate the dimension of the revealed edges. How is the dimension of the revealed edges related to that of the paper ball? Thanks to Emeka Dan-Udekwe for sugesting this exercise. Answer
7. Do the bean bag experiment by counting and record the dimension. Save these bean bags for exercise 11.
8. To what number should the bean bag dimension be close? Answer
9. Explain why the paper ball and bean bag experiments give different results. Answer
10. Which experiment produces a fractal structure? Explain your answer. Answer
11. Do the bean bag experiment by weighing the bean bags. Use the same bags as in exercise 7. Compare the dimension obtained by weighing with that obtained by counting.
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