Name: __________________________
Project for Advance Geometry
Let’s talk about the exciting project we will have in Geometry. You have two options to choose from for
your project. Option A is String Project and option B is “I’ve Got Geometry Bug!. Read the details of each
and choose what works best for you. This project is a major grade and should be taken seriously. This is due
on ____Jan. 27, 2012_(Friday). Last day for late project is Jan. 31, 2012 (Tuesday). Have fun on making
your project!
Option A. STRING PROJECT
Create a design with geometric figures using strings. Create triangles, squares, pentagon, circles and
combinations of these using colored strings, nails and board. Use your imagination in making a design with
geometric figures using ruler, compass, protractor, pencil and paper or using Geometer's Sketchpad
(Computer software) and have fun in seeing your design becomes real using string art.
For more information about string art, I listed some website that may be of help.
Materials
wood or thick cardboard(maximum of 15” by 15”)
5/8 inch nails
colored thread
created pattern/design (3copies)
paint (as needed)
Tools
Hot Glue
Glue
Scissors
hammer
Paint brush (as needed)
Procedures
1.
2.
3.
4.
5.
6.
7.
Create a pattern/design drawn or printed (colored, 3 copies)
Cut out the piece of wood, sand the edges smooth. (max of 15” by 15”)
Tape the pattern to the piece of wood
Put a nail at every point indicated by the pattern
Remove pattern
Straighten nails with pliers
Paint (I prefer white because it makes most colors stand out. Use whatever will look good. Let paint
dry thoroughly.)
8. Tie thread on first nail (preferably embroidery thread)
9. Follow pattern to complete design
10. Tie thread on last nail
11. Place a small drop of glue on knots to hold them tight
12. Cut off excess thread
Here are some good websites to find directions, examples and more!!!
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http://members.cox.net/mathmistakes/bezier.htm - The Mathematics of String Art.
http://www.easycreations.com/ - kits that someone has created and is now making a business by
selling them….look at these for ideas!
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http://www.childs.mccsc.edu/art98/art2p1.htm - see what these six graders were able to make!
http://www.hgtv.com/hgtv/shows_htohm/article/0,2756,HGTV_23316_4062415_011,00.html –
HGTV’s lessons with designerTodd Oldham and actress Elizabeth Berkley
http://www.e-scoutcraft.com/string/flower.html - string art flower instructions!
http://stringart.com/ - looking for intricate designs where color is an integral part…check this site out!
Don’t want to pound nails or push pins? Take a look at these sites for ideas!
http://www.raft.net/ideas/Scalloped%20Circle%20String%20Art.pdf
http://wchow.home.znet.com/SquareArt.htm - who says that string art isn’t practical? Check out this
picture frame made from String Art!
Sketchpad Instruction Videos: Circles for String Art
Angles for String Art
Major Parts of this Project
Three things are to be turned in:
1) your original design on paper. You are to incorporate at least three geometric concepts (i.e. acute,
right, and/or obtuse angles; triangles, circles, quadrilaterals, pentagons, hexagons, and/or other
polygons) into your design and label them on the plan you turn in. Color-code the design that you will
turn in by printing it on a color printer or coloring it with colored pencils - make two copies - one to
turn in with your evaluation sheets and one to use to guide your "nail" placement. Draw in a one line
of symmetry using a dotted line. Label the center of rotation for your rotational symmetry. Make
sure to find its order and magnitude when talking about rotational symmetry and show on your design
how you found it. Label the point about which you can rotate your design when checking point
symmetry. Sometimes the center of rotation and the point in point symmetry are the same. Make sure
that this is noted appropriately. Use one to hand in and one (a photo-copied one) to aid in
nail/pin/hole placement.
2) your completed string art project. The final project can be no larger than 15" x 15" if it is mounted
on a flat surface or it should fit into a 15" x 15" x 15" cube if it is 3-dimensional. Remember to put a
hanger on the back of flat string art (The tab on a pop can nailed to the back works well and can
usually be obtained without an additional cost.) or a string hanger for 3-dimensional projects. Put your
name, grade in high school, and date on the back of your project.
3) the filled out symmetry/shape worksheet giving your completed piece of geometric art a
TITLE/NAME like any great work of art (such as Piet Mondrian’s ‘Composition in Red, Yellow and
Blue’, Monet’s ‘MADAME MONET AND CHILD’, or Picasso’s ‘Glass Vessels”). The worksheets
need to address the shapes that can be found in your design and symmetry that can be found in your
design. Make sure to address the magnitude and the order when you are talking about rotational
symmetry. (See the Evaluation tool!)
STRING PROJECT EXAMPLES:
RUBRICS FOR STRING PROJECT
Name ____________________________________
Title of your String Art: ___________________________________________________
(name it as if you were naming a piece of fine art like a sculpture or painting)
Category
Points
Available
Design: Original and creatively designed
10
Design: Has a minimum of three different
geometric shapes.
12
String Art: Constructed with Geometer’s
Sketchpad OR drawn with math tools
10
String Art: Size: if flat – maximum size is 15" x
15" or if 3-D it will fit into a cube with an edge
of 15"
10
String Art: has a way to hang it
5
String Art: Lines are used effectively in the
design to accentuate and illustrate curves.
10
String Art: Use of color in the final project
10
Title is given for your Project - put it on the
top of this form:
2
Paper – complete the attached form: Paper
addresses the geometric shapes used, all three
types of symmetry, and where they can be found
in your design – shapes have to be made with
nails/pins/holes and used to create curves to
count.
31
Optional Extra Credit: Three dimensional string
art
10 E.C.
Points
Awarded
Comments
Total -->
String Art and Symmetry
100
Name _____________________________
Symmetry/Shape Worksheet for String Project
Choose three of your shapes individually and label them: figure 1, figure 2, and figure 3.
You will be asked to fill out this form for each of your individual shapes and then the string art as a whole.
Fill out this form for your string art:
Figure 1
Line symmetry –
1. Does this figure have line symmetry? (circle one) YES NO
2. Draw the lines of symmetry with dotted lines.
3. How many lines of symmetry does this figure have? _____________
Rotational Symmetry –
4. Does this figure have rotational symmetry? (circle one) YES NO
5. Mark the center of rotation and label the point. The center of rotation for this
(i.e. circle, acute angle, etc.)
Name of this figure :
figure is point _______
Figure 2
6.
What is the order of rotation? ________ What is the magnitude? _________
Point Symmetry –
7. Does this figure have point symmetry? (circle one) YES NO
8. How do you know?
Line symmetry –
9. Does this figure have line symmetry? (circle one) YES NO
10. Draw the lines of symmetry with dotted lines.
11. How many lines of symmetry does this figure have? _____________
Rotational Symmetry –
12. Does this figure have rotational symmetry? (circle one) YES NO
13. Mark the center of rotation and label the point. The center of rotation for this
figure is point _______
(i.e. circle, acute angle, etc.)
Name of this figure:
14. What is the order of rotation? ________ What is the magnitude? _________
Point Symmetry –
15. Does this figure have point symmetry? (circle one) YES NO
16. How do you know?
Figure 3
Line symmetry –
17. Does this figure have line symmetry? (circle one) YES NO
18. Draw the lines of symmetry with dotted lines.
19. How many lines of symmetry does this figure have? _____________
Rotational Symmetry –
20. Does this figure have rotational symmetry? (circle one) YES NO
21. Mark the center of rotation and label the point. The center of rotation for this
(i.e. circle, acute angle, etc.)
String art as a whole
Name of this figure:
figure is point _______
22. What is the order of rotation? ________ What is the magnitude? _________
Point Symmetry - Does this figure have point symmetry? (circle one) YES NO
23. How do you know?
Line symmetry –
24. Does this figure have line symmetry? (circle one) YES NO
25. Draw the lines of symmetry with dotted lines.
26. How many lines of symmetry does this figure have? _____________
Rotational Symmetry –
27. Does this figure have rotational symmetry? (circle one)
YES NO
28. Mark the center of rotation and label the point. The center of rotation for this
figure is point _______
29. What is the order of rotation? ________ What is the magnitude? _________
Point Symmetry –
30. Does this figure have point symmetry? (circle one) YES NO
31. How do you know?
IMPORTANT: Staple your design with your figures clearly labeled, your lines of symmetry dotted, and centers of
rotations clearly labeled. Hand in all of these sheets with your string art on the day it is due!
STUFF TO CONSIDER BEFORE MAKING STRING PROJECTS
Before you begin it will be helpful to find out about the strengths and weaknesses of various materials and
how to avoid potential hazards.
FLAT DESIGNS: Wood works nicely with nails since they can be nailed in tightly and will strong enough
to make sure that string can be pulled tightly. Paint or cover your work area to bring out the beauty of your
design. Place a copy of your design on the work surface and secure it with tape while you attach the nails or
pins or punch the holes for your design. Remove the copy carefully from the work area after you've secured
the nails or (if you think you can) after the string has been added to the design. Decorative nails are available
but remember that they become part of the design. Nail heads can be painted to make the design the focus of
the design. If you use cardboard with holes, use stiff cardboard that will not bend or bow when the string is
woven. A second layer of cardboard on the underside trimmed about 1/4th inch smaller all of the way around
the shape will make it stronger. If colored cardboard is not available paste colored paper on cereal box (paper
board) cardboard and mount this on corrugated cardboard or foam core board. Make all of your markings on
the underside of the cardboard when sewing with your "string".
STRING: String too thin breaks easily; string too thick is hard to
work with and takes away from the intricate designs that you've
created. String or thread that contains polyester tends to stretch over
time so it is NOT a good choice. Embroidery thread and thin string
make good choices because of the availability of vivid colors and ease
of use. Using lengths longer than 4 feet are often hard to work with
because they tend to get tangled. Secure your threads securely with
tight knot (a very small amount of clear-drying glue on the knot will
help to secure it but make sure that it dries completely) or pull the
string through to the back of the design and secure it with strong tape.
For each project, begin the weaving slowly until you become familiar
with the pattern that you’ve created.
If you are making a 3-D design with straws, use thin cotton tatting,
crochet thread, or one strand of embroidery floss. For wood dowels,
cardboard, or nails, these same types of thread or somewhat heavier
cotton crochet thread works well. (Caution: Polyester materials may
sag later because it gradually stretches over time.) Pull the strings
tightly while building polyhedra with the straws and while weaving.
Sagging straws and limp strings detract from the beauty of your
geometric work of art. Winding the string on a spool or cardboard tube
will make working with wood and nails a little more manageable. For
weaving on plastic straws, use NO MORE THAN 4 feet of string on
the needle at a time. You’ll get all tangled up if you do!
COLORS: Your string colors should coordinate with your background color or the colors on your straws.
Contrasting colors make interesting and attractive designs. When using two or more colors of string choose
all bright colors or all pastels – colors with the same tone value. If you will be hanging your design from the
ceiling, make your string a different color than the walls that will be in the same room.
GLUE: Should you need to use glue, white clear-drying glue works best on wood dowels. If you are trying
to get plastic straws held in place, rubber cement works best.
STRAWS: Use a heavy needle and thin thread for dropping the threaded needle through the straws; the
needle may get stuck inside the straw if it is not heavy enough. Plastic drinking straws or stiff round stirring
straws make neater models. Slender straws make neater designs, however, slimmer and longer straws tend to
bend. When you make the holes in the straws, punching them closer together makes them more intricate.
However, if you punch them further apart it helps to prevent them from arching. If straws begin to bend,
insert pieces of coat hangers or thin dowels through the straws. Applying rubber cement will help to hold
them in place.
WOOD DOWELS: The sturdiest 3-D models are made with wood dowels. Making notches takes more
time, but the wood rarely arches during the weaving. The most attractive models have slender edges and
notches close together. Wood dowels make it easier to make larger models that won’t tend to bend or arch.
OPTION B: I’ve got that Geometry Bug!
I've got that Geometry BUG!
Geometry is found everywhere in nature. The insect world provides a nice study of
geometry. Insects constitute between 70 and 80 percent of all known animals. Ever since
the Carboniferous period (200,000,000 years ago) insects have dominated animal life
form. During this early time, dragonflies sped through the air on wings with a spread of two feet! Throughout
time, insects have evolved and changed to meet the demands of their environments. Some insects crawl or hop
on land, some fly through the air, and others live in the water.
Various characteristics of insects differentiate insects from all other
animals. In an insect's adult form, it has a hard outside skeleton called an
exoskeleton, and a body distinguished by three main divisions: head,
thorax, and abdomen. It also has one pair of antennae or feelers on its
head and three pair of legs attached to the thorax. Most winged insects
have two pair of wings attached to the thorax. There are also minute holes
along each side of an insect called spiracles. After doing further research,
you will know more about the geometry and purposes of a bug’s body.
Major Part of This Project
Three things to turned in:
1.
Geometry Bug (object you design with geometrical shapes.
Creating your Bug...
Look at the parts of an insect's body. Can you see geometrical shapes? The body
of an insect has many geometrical properties. In our study of Geometry and Bugs,
you are to use your imagination and your knowledge of insects (including that from
your research homework) to create a fantastic geometry bug. Your bug should use
a lot of geometrical shapes and be colorful and unique since our bugs will only live in our room and
your imaginations. You may use any type of materials to make your bug - let your imagination be
your guide. The bugs are to be made entirely out of geometrical shapes and contain the characteristics of
insects. Your finished bug should fit into a cube with a 10" side and if your bug has wings, its wingspan should
not be larger than 24". Make sure that if your bug is to fly that you include a way to hang it from our ceiling. If
it is to crawl up the wall, there should be some fairly easy way to attach it to the wall, etc.
2. Story about your bug.
Communicating your knowledge...
Write a story about your bug - "A day in the life of my Geometry Bug ". It should be at
least two typed and spell checked pages, double-spaced, and use a normal font size
(around 12 characters per inch). Include the following information...
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Give it a name - hopefully something geometrical!
Identify the shapes and geometrical properties that you used in creating your "geometry bug".
Tell why the bug has the geometrical shapes that you gave it for each of its parts.
Describe where it lives, how it moves, and what it would eat, etc.
Explain what geometrical challenges it faces.
Give a complete bibliography of resources used for the paper and the research questions.
3. Research Paper for “I’ve got that Geometry Bug!” (see attach page)
Materials: anything (you can use paper, plastic bottles, can styrofoam etc
Insect Sites
1.
Iowa State University's Tasty Insect Recipes--Yes, just what it sounds like! Teach your students the importance of insects
in the human food chain in some parts of the world, and get them to try it if you can!!
2. 3D Virtual Insects
3. University of Florida's Book of Insect Records
4. Bugbios.com - This site aims to help you really see insects for the miniature marvels they represent and to understand
how intertwined our cultures have become with these alien creatures.
5. The Bug Page
6. Bug Ranch - Entomology Art - features a collection of entomological art, early engravings, and natural history illustration
7. BugScope - participating classrooms will have the opportunity to control an Environmental Scanning Electron
Microscope to image insects at high magnification.
8. The Creepy Crawly Zoo
9. Class: Insecta - photographs and information culled from the Spencer Entomology Museum.
10. Cultural Entomology - explores how insects affect all facets of the humanities.
Web Directories on Insects....
1.
2.
3.
4.
Entomology - WWW Virtual Library
Iowa State Entomology Index of Internet Resources
Forest Entomology Textbook Challenge for the 21st Century - Fetch21 provides linkages to forest insect web sites
around the world that would be of interest to the undergraduate and graduate students in entomology.
Insects on WWW - Over 2000 insects and entomology related URLs covering almost every aspects of entomology.
Math Sites
1.
2.
3.
Naming Polygons and Polyhedra
Polygons and Their Relations
Symmetry - make sure that you understand all three kinds of symmetry and address them in your research
questions/story!
4. Fr. Magnus Wenninger, OSB, mathematician, builder of polyhedra - Visit here to see some AWESOME polyhedra. Any
bug would be proud to be made from one of these!
5. Unfolding Polyhedra
6. Hidden Polygons
7. Models of Regular Polyhedra
8. Polyhedra and Polygons - from the files of the Geometry Junkyard for help with symmetry, polyhedral models,
9. Circles and Loci
10. Sketchpad Polygons - You could use sketchpad to design your bug!!!
11. Geometry Junkyard! - Great Geometry Resources!
12. Angles in Polygons and Tessellations
Name _______________________________
Research for
"I've got that Geometry Bug!"
DUE: ___________________
Directions: Type your answers to these questions. (25 points)
1.
2.
3.
4.
What is a common insect that has only one pair of wings?
What is the job of the spiracles on an insect?
Why isn't the blood of in insect red?
Draw a line down the center of an insect. What do you notice about both sides of the line? What
geometrical term is used to describe this characteristic?
5. The mouth parts of an insect can be put into two major types o biting and chewing and
o sucking which can also include piercing or lapping.
How does this affect the geometry of the insects mouth structure? Give two examples of insects with
each type of mouth structure.
6. The six legs of an insect are not always identical. Why is this? What kinds of adaptations are made for
different types of tasks such as jumping, flying, crawling, etc.?
7. Often times we look at insects at things that "bug you" or are a nuisance, but they are an important part
of the world around you. Why are insects important in your world?
8. What are polygons? What does it mean to have a closed polygon? a simple polygon? a regular polygon?
9. List the names for the polygons with 3, 4, 5, ... 15 sides. Then find a polygon with more than 15 sides and
write it's name.
10. What is an interior angle of a polygon? Is there a formula for finding the measure of interior angle of a
regular polygon? If so, write it making sure to define the variables.
11. Artists often use geometry when asking to draw or sculpt their impression of something. Find an artist
or two who seems to use geometry to create sculpture. Include
o their name(s),
o the names of some of their art and when they created them,
o how they used geometry in their art,
o their style and/or the art movement that they are associated with, and
o the resource(s) for your information.
12. How does geometry influence the lives of biologists and artists? Why would knowing and being able to
work with geometry make their work more interesting and sometimes easier?
I got this project idea from Nancy Powell and Cathy Denbesten. Thanks a lot to them.
HAVE FUN! 
Sample Projects
I've Got that Geometry Bug!
A Day in the Life of Cone Tail
One day there was a bug named Cone Tail. He was a really smart bug. He
had grown up in Seattle near the Microsoft factory. His owner was named
Kevin. Kevin went everywhere with Cone Tail. They played games together,
went to the park, and Cone Tail even helped Kevin with his homework.
When Kevin had a paper he had to type on the computer, Cone Tail would
help him. One day Kevin got assigned a special project for school. He was
supposed to make his own web page. While he was working on it someone
sent him a file and told him to download it. Kevin, thinking that the file was
harmless, decided to download the file to see what was in it. Once he did his
computer froze up. When he tried typing the computer would make a beeping sound. Kevin restarted his
computer but it didn’t help, the computer just kept beeping.
Kevin called his dad in to see if he could help him fix the computer, because he was an expert with
computers. His father was helping design a new computer for Microsoft. After trying for an hour, neither
Kevin nor his Dad had been able to fix anything. Kevin’s dad told him that when he had downloaded the file
it had probably contained a virus or bug that had affected the computer. Kevin was really disappointed
because he couldn’t work on his project so he decided to watch some television with Cone Tail. After
watching their favorite show, Cone Tail mentioned that he had an idea how to get rid of the bug on the
computer. Before this Kevin had never known but Cone Tail’s favorite food was a delectable computer bug
or virus. Kevin was so excited he could hardly believe his ears. He picked up Cone Tail and raced into his
room.
Cone Tail said that the only way he could get inside of the computer was to go through the floppy disk
opening. He thought it would be a little dark in there so Kevin got Cone Tail a miniature flashlight and
hooked it around his neck. Cone Tail started becoming a little anxious, but Kevin assured him that
everything would be fine and that he had nothing to be worried about. Kevin pushed back the flap to the
floppy disk drive and helped Cone Tail through. As cone tail started going through the computer he started
hearing strange noises coming from one corner. He headed in that direction. When he got there he came face
to face with a giant computer bug. It was one of the biggest ones he had ever seen. It was chewing on one of
the wires that connected the keyboard to the monitor. "That explains why the keyboard was beeping,"
thought Cone Tail. As he approached the bug, the bug got really scared and he started to run as fast as he
could. Luckily Cone Tail was in good shape because he had been doing his daily exercises and he was able
to overtake the computer bug. He wrestled it to the floor, stung it with its stinger, and then ate it up. Cone
Tail started heading back to where he thought the opening was but finally he reached a wall, but he realized
that during his chased he had gotten turned around. He turned a 180 and set out the other way. Finally after a
long walk he reached the opening. When he got there he called out to Kevin and Kevin opened the flap and
helped him out. Cone Tail was so tired he fell asleep in Kevin’s hand. Cone Tail woke up to the smell of
freshly baked chocolate chip cookies, his second favorite food. He and Kevin both stuffed themselves with
cookies and then they started to work on Kevin’s project. On the day when Kevin had to present his web
page to the class he was able to bring in Cone Tail, to whom he had dedicated the page. The whole class
loved his project and his teacher loved his project. He got an A+. To celebrate, Kevin and Cone Tail went
out for Pizza with their friends.
I used many geometrical shapes in the creation of Cone Tail. I used a cylinder, a sphere, a cone and many
different angles. I made the legs that were horizontally across from each other congruent. I also used
rectangular pieces of tape and paper.
I used angles to make the antennas. I used a cone so it would have a pointy back end so it could sting
computer bugs. It uses it’s angular legs to jog and run. It’s only challenge it faces is it can’t get into the
computer unless someone holds open the floppy disk flap.
Bibliography:
Encarta, computer program, 1996.
Fanning, Eleanor, Insects from Close up, 1965.
Geometry for Enjoyment and Challenge, McDougal Littell Co., 1991.
Http://www.mathleague.com.
James/James, Mathematics Dictionary, Van Norstrond Reinhold Co., 1976.
Webster, Merriam, Webster’s 9th Collegiate Dictionary, Merriam Webster Inc., 1983.