**[tippy title=”Problems 1-4″]Problems 1-4**

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.[/tippy]

**[tippy title=”Problems 5″]Problem 5**

Follow the directions; go ahead – pick any two nonzero numbers. You will need a calculator to do the ratios.[/tippy]

**[tippy title=”Problem 6″]Problems 6**

Follow the directions in this problem.[/tippy]

**[tippy title=”Problems 7-11″]Problems 7-11**

Use your calculator to find the ratios and compare with tau (about 1.618). If you obtain the ratio 0.618, reverse the numerator and denominator.[/tippy]

**[tippy title=”Problem 12″]Problem 12**

The answers for this is found by reading the section.[/tippy]

**[tippy title=”Problems 13-20″]Problems 13-20**

See Table 7.2.[/tippy]

**[tippy title=”Problems 21-24″]Problems 21-24**

See the definition of a Saccheri quadrilateral and Figure 7.72.[/tippy]

**[tippy title=”Problems 25-32″]Problems 25-32**

Take a look at Figure 7.71. These problems are designed to improve your ability to visualize three-dimensional objects. Take you time with these problems and ponder your responses before completing the problem.[/tippy]

**[tippy title=”Problems 33-34″]Problems 33-34**

You will need to get a ruler and measure these objects before finding the ratios.[/tippy]

**[tippy title=”Problems 35-36″]Problems 35-36**

You will need a tape measure to measure the distances as shown in Figure 7.65 before finding the ratios. You may need someone else to help you do your measurements.[/tippy]

**[tippy title=”Problem 37″]Problem 37**

Draw a picture to understand the pattern, and then use a Fibonacci-type sequence to answer the questions.[/tippy]

**[tippy title=”Problem 38″]Problem 38**

Draw a picture to understand the pattern, and then use a Fibonacci-type sequence to answer the questions. Use a calculator to find the ratios.[/tippy]

**[tippy title=”Problems 39-42″]Problems 39-42**

Find the requested ratios; you may need to use some algebra (see Examples 1 and 2) in this process. Compare with tau (about 1.618).[/tippy]

**[tippy title=”Problems 43-46″]Problems 43-46**

The answers for these are found by reading the section.[/tippy]

**[tippy title=”Problems 47-48″]Problems 47-48**

You need to have a globe map and a protractor to carry out this activity.[/tippy]

**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/**