Points and Angles Online
December 2001

    Table of Contents:

Zome? A Visual Math Language

Paul Hildebrandt

Zometool, Inc.

 Denver, Colorado

In the movie The Field of Dreams, do you recall Ray Kinsella (played by Kevin Costner) hearing a voice that instructs him by saying, “ If you build it they will come.”?  So Ray builds a baseball field and the players come.  The same could be said of education; if students explore and build models, they will begin to see mathematical properties unfold in front of them.  On Thursday, December 13, 2001, Paul Hildebrandt, president, co-founder and co-inventor of Zometool, will speak at MMC about one of Zometool’s beliefs, “ If you can dream it, you can build it.”  Paul will travel from Colorado to introduce us to Zome and to show us how to begin to explore the concepts that leading mathematicians, scientists, engineers, and architects around the world visualize each day using a Zome connector node. You can use the Zome connector node to build into 62 different directions in space.  This system provides “no limits to discovery,” which allows for thousands of structures that can not be built in any other system.  With Zometool you can even build the perspective cube structure like the one in M. C. Escher’s “Another World”.   It took Paul and his co-founder, Steve Baer, over 10 years to develop the Zome connector node.  Together they designed a set of struts to be used with the nodes.  Paul has given numerous talks and conducted numerous workshops in the United States as well as in other countries for professionals and students of varying grade and ability levels.  Using Zometool, teachers from kindergarten to high school can explore concepts ranging in difficulty from simple geometry to fractals.   If you enjoy exploring numbers and structural concepts, you will be fascinated as Paul Hildebrandt guides us through the world of Zome? A Visual Math Language on Thursday, December 13th at this year’s last meeting at Berghoff’s.

Board Elections

Board members Leona Mirza, Ron Vavrinek, Steve Viktora and Conrad Wayne will be completing their terms this spring. Nominations are open for the three board positions and for the office of President Elect. In
addition to the club's 8 regular monthly meetings, the board holds 4 meetings each year. While responsibilities of board members varies, it is a wonderful experience and an opportunity to work with some
excellent people from throughout the Chicagoland area. If you are interested in running for office or would like to nominate someone, please contact Ron Vavrinek (rvav@imsa.edu or 630/907-5964). Elections
will take place in early spring.

MMC Math Contest No. 17

Five Pentagons and a Constant Sum

                                                           December, 2001


1.   In the above diagram, there are 3 circles on each side of the smallest pentagon, 4 on each side of the next smallest, 5 on each side of the middle pentagon, 6 on each side of the second largest, and 7 circles on each side of the largest pentagon.  Place100 different positive integers in the 100 circles so that the sum of the numbers on each of the 25 sides of the pentagons is the same number.  Record the sum and the numbers in the spaces on the entry form on the next page.

2.   Your score is the sum you use.

3.   The lowest sum wins.  Prizes are as follows:  1st place, $50; 2nd place, $30; 3rd place, $20. In case of ties, prizes will be shared.  Judges are David Witonsky and Zalman Usiskin.  

 4.   Send entries to:

Zalman Usiskin

University of Chicago

5835 S. Kimbark Avenue

Chicago, IL 60637

FAX: 773/702-3114

Entries must be received by 5PM, Wednesday, January 8, 2002.

5.   Any person (student, teacher, or other individual) or class may enter.  Address questions about the contest to z-usiskin@uchicago.edu or call 773-702-1560.  

 Winners will be announced in the February 2002 Points and Angles.


MMC Math Contest No. 17

December, 2001


Five Pentagons and a Constant Sum


Entrant's name                                                   School                                                             



Phone (day)                                        Phone (night)                                               


If student, year in school                     If class, name of teacher                         


e-mail                                                               SUM = _______


                    Smallest                        2nd smallest                                    Middle

                   Pentagon                         Pentagon                                    Pentagon


Side 1 ___   ___   ___          ___   ___   ___   ___            ___   ___   ___   ___   ___


Side 2 ___   ___   ___          ___   ___   ___   ___            ___   ___   ___   ___   ___


Side 3 ___   ___   ___          ___   ___   ___   ___            ___   ___   ___   ___   ___


Side 4 ___   ___   ___          ___   ___   ___   ___            ___   ___   ___   ___   ___


Side 5 ___   ___   ___          ___   ___   ___   ___            ___   ___   ___   ___   ___


                                  2nd largest                                                               Largest

                                   Pentagon                                                               Pentagon


Side 1 ___   ___   ___   ___   ___   ___      ___    ___   ___   ___   ___   ___   ___


Side 2 ___   ___   ___   ___   ___   ___        ___  ___   ___   ___   ___   ___   ___


Side 3 ___   ___   ___   ___   ___   ___      ___    ___   ___   ___   ___   ___   ___


Side 4 ___   ___   ___   ___   ___   ___      ___    ___   ___   ___   ___   ___   ___


Side 5 ___   ___   ___   ___   ___   ___      ___    ___   ___   ___   ___   ___   ___




Answers for the October 2001 puzzle, "What's in a name?"

"It's been estimated that, because of the exponential growth of the world's population, between 10 and 20 percent of all the human beings who have ever lived are alive now.  If this is so, does this mean that there isn't enough statistical evidence to conclusively reject the hypothesis of immortality?"  - John Allen Paulos, Innumeracy, 1988 p.99

(Editor's note:  Unfortunately I ran out of space to include this in the November 2001 issue of Points & Angles.    -Steve)

MMC Scholarship

 The Metropolitan Mathematics Club of Chicago is offering $1,000 in scholarships for high school students who plan a career in the teaching of mathematics.  The selected students, their parents, and their sponsoring teachers will also be invited to the May meeting of the MMC at which time the recipients will be honored.
 The guidelines used for selection shall be:
I. A. Demonstration of overall academic scholarship with inclusion of at least eight semesters of college preparatory mathematics.  (A minimum cumulative grade point average of 3.0, with A = 4.)
 B. A statement of the intention to pursue a career in mathematics teaching.
 C. Indication of participation in extra curricular activities, especially those which may have a positive influence on a teaching career.

II. Applicants must have a letter of recommendation from a member of the Metropolitan Mathematics Club who is familiar with the applicant’s academic performance and his or her potential as a mathematics teacher.

III. Applicants must submit an essay of at most 400 words explaining why they would like to be a mathematics teacher.
 The scholarship award or awards will be determined by a selection committee of MMC members appointed by the Executive Board.  To be eligible, an applicant must submit the application, have an official transcript sent, and request a letter of recommendation from a member of the MMC such that all of the materials are received by the date on the application.
 The committee will establish its own guidelines for evaluating applications, and will make a recommendation to the Executive Board as to the awarding of the scholarship.  No member of the selection committee may nominate nor recommend a candidate.


Application Deadline:  March 18, 2002
Name:__________________________________________  Date:_________________




School Address:________________________________________________________


Home Phone:(____)___________________  School Phone:(____)________________

Sponsoring Teacher (Must be MMC member):_________________________________

Please complete the following:

Overall Grade Point Average:_________  (A = 4, B = 3, C = 2, D = 1, F = 0)

 Mathematics Courses       Grade          Mathematics Courses       Grade

___________________      _____         __________________      _____

___________________      _____         __________________      _____

___________________      _____         __________________      _____

___________________      _____         __________________      _____

Extracurricular Activities:____________________________________________



In addition applicants must also send:

1.  A letter of recommendation from the sponsoring teacher, who is a member
     of the Metropolitan Mathematics Club of Chicago: **

2.  A current transcript for seven semesters of high school.**

3.  An essay not to exceed 400 words on:  “Why I would like to teach

Please send all information to: Conrad Wayne
      Mathematics Department
      Rich South High School
      5000 Sauk Trail
      Richton Park, IL  60471
      phone: 708-679-3150; fax: 708-679-3168
**(Letters of recommendation and transcripts may be sent by separate mail.)
(Photocopy as needed)

To accompany her January 11th talk, “The Mathematics of Frank Lloyd Wright’s Architecture,” Mary Wiltjer will be leading tours of Wright’s Home & Studio in Oak Park and of Wright’s Robie House in Hyde Park on the following dates:

Sunday, January 13th and Monday, January 21st (ML King Day):

Sunday, January 20th 

*All tours will begin at 10:15am. Reservations must be called in to Pat Bowler-Johnson at 847.784-6594 by January 8th. Leave a phone number please. Space is limited. Tours will cost $9.00.


  I cannot believe that it is the holiday time already.  Thanksgiving, for me is a time to say thanks for all whom make our organization what it is.  Thanksgiving is a time for me to say thanks for our profession and how exciting it is every day.  Thanksgiving is a time for me to say thank you for doing all that you do with every child that you come in contact with on a daily basis and for the adults we encourage to become the best that they can become.

Your Board of Directors met last Tuesday, November 13th and discussed many things.  There will be a new teachers (teachers within their first two years) workshop at New Trier organized by Terry Phillips.  There will be more information coming.  Mary Wiltjer will be conducting architectural tours during the weekend following her January talk.  She gives detailed information elsewhere in this issue.  We currently have about 350 members in our organization!  There will be an MMC coffee mug with the MMC logo and Chicago skyline available for purchase early next year (2002).  Conrad Wayne will be continuing to encourage all of us to nominate a high school senior for the scholarship who is very interested in becoming a mathematics educator.  Begin to look at your seniors!  Ron Vavrinek is beginning to put together the ballot for our elections.  If you are interested in running for a board position or for president-elect, please contact Ron at rvav@imsa.edu.  We are also looking at redesigning our newsletter, “Points and Angles”.  Steve Tribbey, editor, began to collect newsletters from other organizations last April at NCTM.  He then began to survey those that came to the November 16th meeting.  So far, people do like the color the Points are printed on and do like the location of the speaker information and the Points from the Interior.  If you have any other ideas, please e-mail Steve at tribbeys@excite.com.  Please e-mail me at ftribbey@d113.lake.k12.il.us with any other ideas or suggestions and I will bring it to our next board meeting on February 11th.

Happy Holidays and see you on December 13th at Berghoff’s!

                                                                                    Fern Tribbey

An Introduction to TI-INTERACTIVE!TM

              Stephanie Casey, mathematics teacher at Deerfield High School, and her husband, Jim, Chemistry and Biology teacher at New Trier High School took MMC members at the Nov. 16 meeting on a visual tour of Texas Instruments’ new software, TI-INTERACTIVE!TM.

            Students need to see a connection between what they are learning and real world applications. One way to do this is through integration of mathematics and science. One tool to help make this connection is TI-INTERACTIVE!TM, a document-creation program that features graphing calculator capability (all TI models from the 82 through the 92+), CBL and CBR links, and a word processor (basically WORD) with a direct link to the Internet. Texas Instruments developed this software for teachers who found they need more technology resources because students are coming to them with so much more background in technology. Another factor in the decision is that schools continue to become better equipped to use technology.

            Stephanie demonstrated an activity she uses in her AP Statistics class that had students examine the relationship between body temperature and heart rate for both men and women. The software makes it very easy to download data directly into lists in the program, similar to the 83 and then put the data into a histogram or scatterplot or some other stat plot. But, as Stephanie demonstrated, TI-INTERACTIVE!TM has enhanced capabilities in terms of labeling the graph title, axes labels, labels for specific parts of a graph as well as the use of color. Jim demonstrated a lab experiment that he has students perform in his Chemistry class that deals with changes in water temperature as ice is melted over a Bunsen burner. A CBL and temperature probe are used to collect the data which is then transferred directly to lists in the software. What Jim really likes about TI-INTERACTIVE!TM is that after his students have analyzed the data graphically, they can used the word processing capabilities to write up the report as part of the same document. Stephanie then demonstrated an experiment she has her students perform involving ball displacement and velocity using a CBR. After displaying some sample data in a scatter plot, Stephanie showed a feature of the updated version (1.1) called the “slider” feature. This feature allows the user to enter the general form of an equation, such as y= ax2 + bx + c, and set up a range of values for each of the constants. By sliding the “slider” bar with the mouse, the user sees what effect each of the constants has on the function. It is also possible to set up a tangent line to a curve and while sliding the line along the curve, observe the changes in the equation of the tangent line.

            In closing, Stephanie and Jim informed everyone that there are sample CD’s to try out TI-INTERACTIVE!TM as well as a sample activity from TI’s EXPLORATIONS Workbook for TI-INTERACTIVE!TM. For those MMC members who were unable to attend this very interesting and informative presentation by Stephanie and Jim Casey, you can download your own free sample from the Texas Instruments website.  <http://www.ti.com/calc/>

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