The Nature of Mathematics, 12th Edition
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Section 8.3 Homework Hints

    Problems 1-2
    There are many problems throughout the text labeled IN YOUR OWN WORDS. Just relax; do not be afraid to give your opinion. For the most part, these questions do not have "right" or "wrong" answers. You should spend about five minutes in answering each of these questions.
    Problems 3-4
    Compare with Figure 8.37. Think of each figure painted on a piece of elastic inner tube. If you can stretch into the other (without tearing), then they are equivalent. For example, in Problem 3, Figure A can be transformed into Figure F.
    Problems 5-6
    Review the definition of a closed figure.
    Problem 7
    Compare with Figure 8.37. Use the font shown in the book to make your decisions, because some fonts can change the topological properties of certain letters.
    Problems 8-9
    Compare with Figure 8.38.
    Problems 10-15
    These problems explore the concept of inside/outside.
    Problem 16
    Read the section of the text discussing the four color problem.
    Problems 17-18
    These problems can be done by experimentation. Simply try drawing and coloring these maps.
    Problem 19
    This problem explores a variation of the four-color problem. Read the section of the text discussing the four color problem.
    Problem 20
    This problem explores a variation of a fractal curve. Read the section of the text discussing the fractal geometry.
    Problem 21
    This problem explores a variation of a tessellation. Read the section of the text discussing tessellations.

    Note: Homework Hints are given only for the Level 1 and Level 2 problems.

    However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 problems, check some sources for help on the internet (see the LINKS for that particular section. As a last resort, you can call the author at (707) 829-0606.

    On the other hand, the problems designated "Problem Solving" generally require techniques that do not have textbook examples.

    There are many sources for homework help on the internet.

    Algebra.help
    Here is a site where technology meets mathematics. You can search a particular topic or choose lessons, calculators, worksheets for extra practice or other resources.
    http://www.algebrahelp.com/

    Ask Dr. Math
    Dr. Math is a registered trademark. This is an excellent site at which you can search to see if your question has been previously asked, or you can send your question directly to Dr. Math to receive an answer.
    http://mathforum.org/dr/math/
    Quick Math
    This site provides online graphing calculators. This is especially useful if you do not have your own calculator.
    http://www.quickmath.com/

    The Math Forum @ Drexel
    This site provides an internet mathematics library that can help if you need extra help. For additional homework help at this site, click one of the links in the right-hand column.
    http://mathforum.org/

    Mathematics Home Page
    Access the Clemens and Alcuins Library of CSB/SJU and find one of the world's best collections of mathematical internet sites.
    http://library.csbsju.edu/rqs.phtml?subject_id=32

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