**Project
List**

**Ch 1 Photo Project: **Find a picture on the internet (or scan
one from a book or magazine) that appears to contain lines, points
and angles, like the bridge picture on the website in chapter 1.
Paste your picture into a Geometer's Sketchpad file. Draw each of the
6 basic geometric elements on top of the picture, and label them as
shown in the example on the website in chapter 1.

**Ch 2 Graphics Project:** Create a symmetrical geometric
design, with compass and ruler, or using geometry software. Begin by
constructing a simple geometric shape (a triangle, for example) and
then repeat the shape in a symmetrical pattern. an example is shown
on the website in chapter 2. You can experiment with colors, and
create a beautiful design. If you have access to a paint program,
such as SuperPaint, very beautiful effects can be created by copying
and pasting a black and white line drawing from GSP (hide the points
first) into the paint program, and then painting the design in the
paint program where you have many color and effects options.

**Ch 3 Research Project:** Do some research of your own on the
internet, on the History of Geometry. I would suggest you begin with
the links on the website in chapter 3, to get warmed up. Then do a
Net Search using Geometry as the Key Word. Write a 2 to 3 page report
on what you discover. Please do not just copy and print pages off the
internet. You should search, read what you find, think about it, and
write a summary/discussion of what you find. You may include direct
quotations (a few sentences or even a paragraph), but be sure to put
these portions in quotation marks, and include the web addresses to
give credit to your sources as was done on the website in chapter 3.
You should include some images, but if you copy the images from the
internet, you must give credit as was done on the website.

**Ch 4 Tangrams Project:** Design your own tangram challenge,
using a ruler and compass, or geometry software. Create a second page
with the solution to your challenge.

**Ch 5 Origami Project:** Fold a square piece of colored, good
quality paper, to create an interesting Origami. It can be anything
you like: an animal, a bird, or just an abstract three-dimensional
shape. Then create a step-by-step set of instructions that someone
else could follow. You may look at the step-by-step examples that you
saw on the web pages using the links in chapter 5, but use the
"cricket" example on the website for chapter 5 to guide you, using
geometric terms to describe the steps. Your instructions do not have
to be as complicated as the cricket example.

**Ch 6 Spiral Project:** Write an illustrated report 2-3 page
report on any one of the Right Triangle, Sequences, or Spirals topics
in chapter 6 on the website. Your report can be written using
information you found on the internet and/or books. Keep in mind that
this report must be your **own** work, and not just copied and
pasted from the web. If you do use a sentence or two of someone
else's work, be sure you include their name and the name of their
book or web page to give them credit.

**Ch 7 Drawing Project:** Learn more about 3-D drawing by going
to the Math Forum website and reading all the pages at**
**http://www.forum.swarthmore.edu/workshops/sum98/participants/sanders
Then do the following two things as your Project: 1) Find a picture
of a building on the internet. (You might strat with a net search
using the word "architecture") Be careful to choose a picture in
which you can see the lines vanishing as in the examples on the forum
website above, as if towards Vanishing Points. Your assignment is to
use a pencil and ruler (or geometry softward) to draw a simple
building or buildings, of your own design, in perspective.

**Ch 8 Tessellation Project**: Create a tessellation of your
own, using the method described in the web pages. Start with a square
or hexagon, and create an interesting shape as descrived in the web
pages. Use tracing opaper to trace your shape, and create a
tessellation.

**Ch 9 Indirect Measurement Project:** Choose a tall object to
measure, using indirect measurement. This object must be something
that cannot simply be measured with a ruler or tape measure; it must
be something that is very tall, and inaccessible, such as a tall
flagpole at school, a high-rise building, or a steep cliff. It also
needs to be in a relatively flat field, park, or section of town, so
that its shadow will be measurable. This may depend on the time of
day that you do your measuring, so you will probably need to make
some observations in different parts of town, and at different times
of the day. Of course the shadows will be shortest near noon! Measure
the length of your object's shadow, and measure the length of your
own shadow as you stand nearby, or measure the length of the shadow
of a yardstick held vertically nearby. If you use your own shadow,
you may need an assistant, and you will need to know your own height.
Draw careful sketches, and calculate the height of your object, using
the method shown in the web page. Write a careful explanation,
including any problems you encountered. Tell us where and what your
object is. Show your calculations. Be sure to use accurate values in
your calculations, and do not round any numbers until you get your
final answer. Presentation is always important; do a nice job on the
drawings and the written work, so that it shows pride in your
work.

**Ch 10 Graph Project:** What activities make up your daily
life? Collect data on this topic, and design a circle graph. To
collect the data, keep a journal for one week of how much time you
spend on each of your activities: you might include such categories
as sleeping, doing homework, time spent in class, etc. Organize the
data in groups with the hours and fractions of an hour. You might
need to combine some of the smaller groups into a more general
category. You should have at least 8 categories. Now you need to
divide the circle into portions for the categories. For example, if
you spend 8 hours sleeping, then that is eight twenty-fourths of the
day, and would then be eight twenty-fourths of the 360 degrees in a
circle. Some example calculations are shown below. After calculating
the sizes of the sectors of the circle for each of your daily
activities, draw a large circle on a nice piece of unlined paper or
poster board, or use a painting program. Do not use a computer
program that does all the calculations and graphs for you! Use a
protractor (or the measuring system in your painting program) to
carefully construct the angles. Label your graph, using the colorful
graph called "Age of Users" on the website, as an example. Do your
best work; make this a beautiful and informational graph!

**Ch 11 Architectural Design Project: **Do some research into
the costs of real estate in your neighborhood. Read the real estate
ads in the newspaper, visit some Open Houses on Sunday afternoons.
The prices of houses depend on their location, the size of the lot,
the "attractiveness" of the house, and the size of the house.
Sometimes building a new house can be less expensive than buying one
that has already been built and landscaped. This of course depends on
the selling price of a vacant lot, and the cost of constructing the
new house. Currently, for "average" quality construction in Hawaii,
one can expect to pay about $100 per square foot of interior space,
and $75 per square foot for lanai or deck space. Calculate the cost
of building the house shown in the floor plan below. This floor plan
is drawn to the scale 1/8" = 1', so you will need to print the
drawing, then measure the overall lengths and width of the rooms with
a ruler, and write proportions to find the lengths and widths in
feet. Then find the areas of the rooms, total them, and multiply by
the construction costs. Show all your work clearly and neatly on the
paper with the drawing. The second part of the project is for you to
design your own home! Pretend you have a budget of $215,000 for the
construction, and don't spend any more than that! Use the approximate
construction costs of about $100 per square foot of interior space,
and $75 per square foot for lanai or deck space. Draw your home at
the scale 1/8"=1', label the rooms, and show your calculations.

**Ch 12 Castle Project:** Do some research on the net, and find
some images of castles. Read some information about the castles, and
explore any aspects that interest you. Then design and create a 3-D
drawing of your own castle, using geometric solids. You must have at
least one each of the four solids we have studied: Prism, pyramid,
cylinder, cone. Then find the volume of the solid portions of your
castle. Be sure to write all formulas, and show all your work!