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Topic: World Construction
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Evelyn Sander

Posts: 187
Registered: 12/3/04
World Construction
Posted: Apr 1, 1993 7:01 PM
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Starting this month, I.T. alumni will go to elementary and
junior high schools all over Minnesota for the first part
of the construction project. The students will cut and paint
1620 triangular panels, each approximately one yard across,
which will eventually make up the globe.

One May 4, the students will come to the university put
all the panels together to build the earth. The construction
will involve a bicycle powered hydrolic lift, enabling the
students to be responsible for every part of the project.

This new world project is a quite interdisiplinary effort,
calling for interaction between engineers, such as organizer
Bryan Beaulieu, elementary and junior high teachers,
students, I.T. alumni, and, as you might expect by the
newsgroup choice, geometers.

Stuart Levy of the Geometry Center got involved with the
project because in order to use flat material to build
a sphere, someone needs to calculate the geodesic structure.
I spoke to Mr. Levy this afternoon about the project. He
gave me some of the particulars of working on this applied
project. It is quite intriguing, especially since it is
somewhat rare for engineers and geometers to work together,
so concerns such as strength of construction and size
of panel are easy to forget.

The material used is a thin plastic which comes in one
yard sheets. In order to maximize the stability of the
globe, it was best for the panels to be triangles. Under
these conditions, Mr. Levy came up with the following
triangulation scheme: starting with an iscosohedron, split
the faces nine-fold, slightly raising each of the new
triangles to give a closer approximation of the sphere.
Use two successive applications of this process to get the
proper size of panels.

After designing the triangulation and underlying structure of
the earth, the next step was projecting maps onto each
of the panels. The students will use these maps to paint
the panels with rivers, other geography, as well as
political boundaries. This involved choosing the best
projection to use, which turns out to be the stereographic
projection. In order to make a map which is larger than one
panel, a better choice of projection is one which unrolls
the surface onto a tangent plane while preserving arclength.
On a larger map, the stereographic projection distorts size
in a distracting way.

This program is an exciting way to bring people of all
ages and many diciplines together for a common purpose.
If you are in the area on May 4, come to campus to
watch the final construction of the world.

From usenet Sun Apr 04 13:47 PD 1993
From: Dover-Sherborn High School <>
Newsgroups: geometry.pre-college
Date: 04 Apr 93 13:47 PDT
Subject: Re: Geometry Projects
Message-ID: <>
References: <1lomd2$>
Sender: Notesfile to Usenet Gateway <>
Nf-ID: #R:1lomd2$
Nf-From: cdp.UUCP!doversherhs Apr 4 13:47:00 1993
Lines: 347

April 4, 1993

Dear Geometry Forum Readers,

This is a fairly long entry. It includes:
I. a project design outline and project evaluation criteria
II. students' project proposals and questions - first draft
III. the classes' regular evaluation model

If you have the time and interest the we would like your responses
to all three, but particularly to the project proposals. Any ideas,
resources, questions, and constructive criticism are welcome.

Our audience will include the entire community - each year the
school sponsors a day when students exhibit their best work for
teachers and parents.

Please address any comments to the students.


Keith Grove
Mathematics Teacher-Dover Sherborn High School, Dover, MA

I. Geometry Projects - Design and Evaluation

When writing your proposal, please address the following list of
considerations. Feel free to list and address other considerations as
you discover them.

Ideas to keep in mind when designing your project.

1. What will your product look like? (identify the characteristics of
your project)
- Who is your audience?
- What do you intend to do with your product?
- How do you intend to present your product?

2. Questions to consider:
- What is your project's relationship to geometry?
- Consider the usefulness of your results.
- What are the possibilities of using your results?

3. Develop a time line for your project.

4. Decide which members of your team will perform each tasks.

Evaluation Criteria:
1. creativity
2. meaning or relevance of the results to your lives
3. general interest
4. attention to detail
5. neatness of presentation
6. choice of presentation
7. accuracy

II. Students' Proposals and Questions - First Draft

Children's Toys: Kristen, Elise, and Tracy
We propose to make two children toys. The toys will consist of
different geometric shapes made of different materials. Is there a
place where we can get any materials for the toys? If the toys are
successful we propose that we try the toys out on the little kids in
the child development center (in our school) and try to send them
to a toy manufacturer. We hope these toys amuse the children and
please them.

Pool Table: Rajiv, Jim, Becky, and Andrew
We are going to show the relevance of geometry in the game of
pool. We are going to show how reflection is the major factor of
playing pool. we can teach the viewing audience of the eduation of
pool in form of a video.

Scale Model Auditorium: Rajiv, Jim, Becky, and Andrew
We are going to construct a model of the new Boston Garden and
how we would envision it. We will show the geometry of building
an auditorium in scale and proportions.

Sailing: Van
I would like to use geometry to design a sailboat of same sort. I'm
looking for some of the basic principles of sailboat design. I'll try
to make a small model of the boat I design. I would also like to
know what materials are easily available and easy to use to make a
small model. I would like to find out some of the formulas used in
sailboat design to possibly use.

Construction of a Geodesic Dome: Judd, Alex, Carey
We will attempt to construct a Geodesic Dome. It is planned to be
around eight feet high and eight feet in diameter. We will
construct it with a wood frame and ply wood floor with linoleum
supported by cement blocks to prevent rotting. The frame will be
covered midway with plywood and midway to the top with
Plexiglas. In the end, this will be used as a small greenhouse. The
purpose of this project is to experiment with the geometry of
construction. This will be worked with until the first week in June.
Our progress on this structure will be videotaped and
photographed to show the different stages. The materials we will
need are the following: tools, screws, nails, 8 small hinges, 2 X 4's,
plywood, 10 cement blocks, Plexiglas, linoleum. Please respond to
this message with any ideas, pictures, or materials that can help us
fulfill our ideas for the project. If you do have materials that you
are willing to donate, please leave your phone number or call (508)
785-1561; ask for Judd.

Gingerbread Village: Krista and Sara
We want to make a gingerbread village. We'll build small
gingerbread houses. We're going to name all the geometric figures
that apply to our house. We'll build it with candy and gingerbread
that have unique and different shapes. Afterwards, we'll show our
village to the class and let the class eat it. We were wondering if
any other people had the same idea as us in doing this project.

Video of Boston Trip: Danielle, Erin and Alissa
We are working on a trip to Boston.(20 miles away) We will go
into Boston with a video camera. Our goal is to plan a field trip to
Boston for our class. We will go in before to plan the day and time
it. In doing that we will also video tape the geometry we see in the
specific sites we want to visit in Boston. Hopefully, we will find
informed people at the specific sites to interview. We are
considering visiting: Omni Theater, Boston Garden, State House,
Faneuil Hall, Cheers, and Back Bay (architecture). My friend will
accompany us through the Back Bay, as someone informed of the
architecture. We will then present the video to the class, so they
see the geometry. The next step is to propose a field trip to our
headmaster. We will also need to find chaperones, because we will
be taking the T in Boston. We hope that we will physically be able
to show our class the geometry of Boston. Basically, we are asking
what you would suggest we look for as the non-obvious geometric
things in Boston.

Telecommunication: Stephanie, Jen, and Lynn
Study and learn about telecommunication. Start conversations
with geometry students from foreign countries. We want to find
out how geometry is related to telecommunication. What is

Photography and Painting: Hilary, Dan, C.C., and Stephanie
We are sophomores at Dover Sherborn High School and are
studying geometry. We are creating a project dealing with
paintings and photographs and trying to apply it to geometry. We
want to make a book with paintings and photographs and analyze
them using geometry concepts. Has anyone done a project similar
or has any suggestions? If you have any please respond.

Aspects of Telecommunication: Charlie, David, and Tom
How it works? What it is? How dimensions are crossed in
telecommunications? How cyberspace is defined? I want to pose a
question of how geometry is related to telecommunications ... in
general, and specific ways? Some other questions I might want to
pose would be: How geometry is related to sensory depravation
tanks? What are several alternate dimensions? How does
cyberspace relate to virtual reality?

Photography: Joe and Eric
For our project we are examing the geometric shapes around the
school building. By taking picture and examining the architecture
we want to learn more about the engineering of this school. We
would like to see if you have any more ideas of geometric areas in
the school to look at? Are there any parts of a building such as this
which are less obvious in examing engineering?

Sound Maps (1): Paul, Rachel, Noah, Amy, Emily
We have different ideas about location of where to do our sound
maps. In the hallway during school and recording what we hear
from which direction we hear it. (with eyes closed) Also in
downtown Dover, or the roof of one of our houses, and in the
woods. On our recordings on paper, that are not 3-D, we will draw
the sounds on translucent paper (tracing) and put them together
so they over-lap. We would also make a 3-D model (from a coat
hanger as a mobile) creating an image of real life. These all would
include location of sounds, origins of sounds, and color coded

Sound Maps (2): Paul and Noah
We are going to listen to music at different tones, places and we
will experiment with different angles of the speakers and what the
different angles result in. We will map out the bass tones, treble
tones and how the sounds differ at different places in the room.

Geometry Relativity: Dan
My project is basically geometric relativity in normally appearing
occurrences, especially through the use of photography. Using this
medium I hope to focus on factors such as distance, length,
dimension, angles, and shadowing. From there I would consider
and compare geometric consequences and causes in these images.

Snowboards: Alex, Eric, and Tim
In our project we will be connecting the shape and construction of
a snowboard with geometry or at least trying to. Also we would
like to consider the physics of the speed and momentum used to
jump and carve down a hill (carving is a way of turning that will
be more explained in depth during our project). We are having
some trouble with the physics aspect of our project. If anyone has
any ideas to help us, it would be greatly appreciated. Thank you.

III. Regular Class Evaluation Model

Goals of the assessment process:

Students will eagerly anticipate assessment tasks as opportunities
to produce something useful - a plan, a portfolio, a report, or
results of an investigation.

The assessment process is a means to ... tell us where we are ...
develop habits of mind ... set ourselves up for better results in the
future ... develop more interesting problems ... develop vocabulary
... tell us how well we are working together.
I. Mathematical Problem Solving, Reasoning & Connections ........
1 2 3 4 5
%I'm using, with increasing confidence, problem-solving
approaches to investigate and understand mathematical content.
%I'm aware of the strategies I'm using to solve problems. %If
necessary, I change or modify my strategy in the middle of my
work. %I understand what I'm doing -- I'm not just going through
the motions. %I have mastered the material. %I'm making and
evaluating mathematical conjectures and arguments. %The work I
do reminds me of work I've done before. %I think about whether
my answers make sense. %I can give reasons for choosing the
strategies I use. %I eventually get most of my work correct. %I am
able to explain the rationale for each answer.

II. Mathematical Communication ..................................1 2 3 4
%I discuss mathematical ideas and make convincing arguments. %I
reflect on and clarify my thinking about mathematical ideas. %I
understand what is discussed in class. %I can explain my thoughts
and strategies in class. %I ask questions for clarification and I ask
"What if ... ?" questions. %I participate to the best of my ability.

III. Mathematical Disposition ...................................... 1 2 3
4 5
%I'm developing personal self-confidence and a disposition to seek,
evaluate, and use quantitative and spatial information in solving
problems and in making decisions. %I'm developing flexibility,
perseverance, interest, curiosity, and inventiveness. %I feel like I'm
doing well in class. %I'm better now at solving math problems than
I was in September. %I work hard to solve math problems. %I try
more than one idea before I give up on hard problems. %I seek out
differences of opinion. %I make sure others mastered the material.
%I avoid interrupting. %I avoid put-downs. %I actively listen.

IV. Small Group
............................................................... 1 2 3 4
%We establish effective procedures for accomplishing our work.
%Everyone understands the purpose of our tasks. %Everyone stays
on task. %Everyone works together on the same problem. %Each
question is understood by everyone. %Each person contributes her
or his ideas. %Everyone understands and takes a turn explaining.
%We actively listen to each other. %We seek out differences of
opinion. %We encourage each other to participate. %We express
support and acceptance of each other. %We have fun!

V. Class
............................................................................ 1
2 3 4 5
%TIME CONSIDERATIONS %Are you on time each day? %Are others
in the class on time each day? %Does class start promptly? %Is class
time being used effectively?
%PREPARATION FOR CLASS %Are you prepared for class each day?
%Are others prepared for class each day?
%ACTIVE LISTENING %Are you listening to the other members of
the class? %Do you feel heard by the other members when you
%PARTICIPATION %Are you participating in group problem solving
discussions? %Are other members participating in group problem
solving discussions?
%UNDERSTANDING %Do you understand the class discussions?
%Does every member of the class understand the discussions?
%RESPECT %Do you respect your own behavior and attitude? %Do
you feel your contributions are respected? %Do you respect the
contributions of others?
%Your base-line numbers were negotiated at the end of the
preceding term. At the end of this term we will negotiate in each
Journal Entries:
%Please answer the following questions at the end of the term:
%What do you do particularly well?
%What, if anything, hinders your success?
%What could you do differently to have greater success?

%Do you perform at least one of the following roles or tasks for the
class? Which one(s) and what is your evidence?
Organizer - makes lists, gives directions, lines up materials.
Encourager - shows enthusiasm for people's ideas.
Idea Person - comes up with a lot of suggestions, or with one very
good one.
Good Humor Person - keeps the activity fun by making funny
remarks in a way that keeps people enjoying what they're
Cooperator - responds to organizers, who can't get anything done
unless there are good cooperators in the group.
Listener - listens intently when people give ideas, so there is a
sense of calm and concentration in the group.
Stick-to-itive Person - when the going gets tough, these people
stick in there and keeps thinking, listening, trying,
Problem-finder - contributes by seeing what's wrong with the
way the group is solving the problem.
Detail-detective - notices little things in the instructions or in the
problem-solving method that are important to pay attention to.
Clarifier - uses words well to explain what other people don't
Includer - makes sure everybody gets a chance to talk.

%How do you feel about yourself as a math student? Explain why
you feel that way. What would the rest of us see that would
correlate with what you are feeling about yourself?
%Are you comfortable with the procedures and the leadership of
the class?

Small Group Questions:
%How are procedures for solving the problems established?
%How is leadership established in the group? What forms did it
%Does everyone's ideas get heard and used?
%What effect does time have on your group process?
%What is most frustrating about the experience of working in
%What kinds of contributions do people make? (roles played, forms
of participation, styles of communication)
%What helped the conversation? What hindered the conversation?
%What do you want to say or do in the group that you don't say or
%What territory does the conversation cover?
%What questions aren't asked? What isn't discussed? What is
passed over too quickly?
%From whom do you feel the most support in the group? How is
that support given? How important is it to feel supported by others
in the group?

If thisP.sS. If this comes through as scrambled as it appears on my screen - I
will try again. ... Keith

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