**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 linksĀ in the right-hand column.

**http://mathforum.org/**

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.Problem 5

Follow the directions; go ahead – pick any two nonzero numbers. You will need a calculator to do the ratios.Problems 6

Follow the directions in this problem.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.Problem 12

The answers for this is found by reading the section.Problems 13-20

See Table 7.2.Problems 21-24

See the definition of a Saccheri quadrilateral and Figure 7.72.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.Problems 33-34

You will need to get a ruler and measure these objects before finding the ratios.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.Problem 37

Draw a picture to understand the pattern, and then use a Fibonacci-type sequence to answer the questions.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.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).Problems 43-46

The answers for these are found by reading the section.Problems 47-48

You need to have a globe map and a protractor to carry out this activity.

**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.Problem 5

Follow the directions; go ahead – pick any two nonzero numbers. You will need a calculator to do the ratios.Problems 6

Follow the directions in this problem.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.Problem 12

The answers for this is found by reading the section.Problems 13-20

See Table 7.2.Problems 21-24

See the definition of a Saccheri quadrilateral and Figure 7.72.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.Problems 33-34

You will need to get a ruler and measure these objects before finding the ratios.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.Problem 37

Draw a picture to understand the pattern, and then use a Fibonacci-type sequence to answer the questions.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.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).Problems 43-46

The answers for these are found by reading the section.Problems 47-48

You need to have a globe map and a protractor to carry out this activity.**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 linksĀ in the right-hand column.

**http://mathforum.org/**

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.

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

Follow the directions in this problem.

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.

The answers for this is found by reading the section.

See Table 7.2.

See the definition of a Saccheri quadrilateral and Figure 7.72.

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.

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

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.

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

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.

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).

The answers for these are found by reading the section.

You need to have a globe map and a protractor to carry out this activity.