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The Newsletter for Advisors of Student Chapters
of the Mathematical Association of America
Spring 2001
MAACSC ® MAACUSAC
What's in a name? In the case of the MAA committee, which produces this
newsletter, the name is a reflection of the committees responsibilities.
These responsibilities were recently expanded by the MAA Board of Governors,
which passed a resolution changing the name of the committee from the MAA
Committee on Student Chapters (MAACSC) to the MAA Committee on Undergraduate
Student Activities and Chapters (MAACUSAC) and broadening the charge of
the committee. This expanded charge is "to encourage and assist colleges
and universities in fostering MAA Student Chapters and to arrange educational
and social opportunities and activities at national and section meetings
for undergraduates interested in the mathematical sciences."
Joint Winter Meetings in
New Orleans
The skies were often gray, and the temperatures a bit on the chilly
side, but the hospitality of the Big Easy was warm throughout the joint
winter meetings January 10 through 13. The full report on student activities
at the winter meetings on page 2 in the New Orleans News.
Madison Mathfest
Mathfest 2001 will take place in the heart of America's dairyland, Madison,
Wisconsin. For full details on activities for students at Mathfest see
Whassup in Madison on page 4.
What's inside?
New Orleans News:
MAA Student Lecture
Mathematical Experiences
Outside the Classroom
2
Abstracts:
New Orleans
7
Washington, DC
11
Whassup in Madison:
MAA Student Workshop
5
MAA Student Lecture
5
Call for Student Papers
6
Other Student Activities
6
Contact Information
15
New Orleans News
MAA Student Lecture
Do you have difficulty dealing with the many choices you are faced with daily, and making decisions about them? If so, then the MAA Student Lecture would have been the event for you to attend in New Orleans. An audience of approximately eighty people was present to listen to Dr. Ralph L. Keeney, a leading thinker in the field of decision theory, talk on "Building and using mathematical models to guide decision making." Dr. Keeney is a Professor in the Marshall School of Business and in the school of engineering and a researcher affiliated with the Center for Telecommunications Management at the University of Southern California. He did his undergraduate work in engineering at UCLA and received his Ph. D. in operations research from MIT in 1969.
Dr. Keenny's presentation was divided into two parts. In the first part he discussed the building of mathematical models through a process of quantifying the desirability of various outcomes and the subsequent construction of a choice function. The second part of the talk provided several examples of the speaker's theories on decision making being put to work. Among these was his work with American Express to help the company increase its market share and his work with the U.S. government in choosing a site for a national nuclear waste repository. Dr. Keeney remained after the talk to answer questions from
the audience. His talk provided students and professors with an outstanding
example of an application of mathematics outside the traditional domains
of the field.
Mathematical Experiences
for Students Outside of the Classroom
On Friday afternoon eight presenters shared various ways to provide mathematical experiences for student outside of the classroom. This was the second year that such a session has been held at the winter meetings, and it was well attended, with about forty people in the audience for each of the fifteen-minute presentations. The eight presenters are listed below, along with the title of their talk. For more details on the presentations this year and last year see pages 7 through 15 for abstracts of the talks from these sessions.
Student Hospitality Center,
The Student Hospitality Center in New Orleans was frequented by students and advisors. Katarina Briedova from the MAA headquarters provided many helpful handouts for the students. Students stopped for refreshments, met each other, and informally discussed events at the meeting. The Student Hospitality Center provided a place for students to meet other students, get information about the meetings and simply relax for a while.
Advisors of MAA and Pi Mu Epsilon Student Chapters also met in the Student
Hospitality Center for the Advisors Breakfast during the winter meetings.
In an engaging session in New Orleans, dozens of professors discussed what
is working in their Student Chapters. Jim Gandorf from MAA headquarters
also addressed the group and mentioned some of the computer related enhancements
going on with the MAA which are pertinent to students and advisors.
AMS/MAA Invited Address
by Dr. Jeffrey Weeks, MAA Student Workshop Presenter
at Mathfest 2001
On Wednesday, January 10, Dr. Jeffrey Weeks gave the AMS/MAA Invited Address on Measuring the Universe. Dr. Weeks will be the presenter of the MAA Student Workshop at the Madison Mathfest, and those who attended his presentation in New Orleans will be looking forward to the Mathfest student workshop.
The grand ballroom of the Sheraton New Orleans was packed for this highly
entertaining presentation in which Dr. Weeks explained how the microwave
background radiation of space can be used to help answer questions about
the curvature and topology of space. A related fundamental question is
whether the universe is finite or infinite. Dr. Weeks explained how inhabitants
of a finite universe might have the illusion of living in an infinite universe
because they see repeating images of themselves and other objects. A selection
of wraparound tic-tac-toe, mazes, and other games that illustrate this
can be found at www.northnet.org/weeks/TorusGames.
For more information on the MAA Student Workshop to be presented by Dr.
Weeks, see page 5.
Plan to attend
Mathfest 2001
Madison, Wisconsin
August 2 through 4
Activities for Students at Mathfest can be found in Whassup in Madison on page 5
Whassup in Madison
Ranking College Football Teams: MAA Student Lecture by Rhonda Hatcher
With the beginning of the college football season less than a month
after Mathfest 2001, Dr. Rhonda Hatcher will provide a timely discussion
of ranking the teams on Saturday, August 4, from 3:00 to 3:50 p.m.
Professor Hatcher earned a B.A. in mathematics from the University of Colorado at Boulder in 1980 and a Ph.D. in mathematics from Harvard University in 1987. Her research specialty is number theory. She taught at St. Olaf College from 1987 to 1990 and is currently on the faculty of Texas Christian University.
Professor Hatcher has been involved in many activities involving students and teaching. From 1992 to 1996 she was the co-principal investigator for a National Science Foundation Research Experiences for Undergraduates project at TCU. She was an instructor in the Summer Mathematics Program for Undergraduate Women at Carleton College in the summer of 1999. Since 1992, she has headed workshops for 7^{th} and 8^{th} grade girls at Expanding Your Horizons Conferences at Texas Wesleyan University. For the past three years she has served as a lecturer in the TCU Advanced Placement Summer Institute for Secondary School Teacher. Professor Hatcher recently co-authored, with George Gilbert, a mathematics textbook for liberal arts students entitled Mathematics Beyond the Numbers.
Professor Hatcher won the 1994 TCU Deans' Teaching Award and the 1997
TCU Honors Professor of the Year Award. In 1998, the Mathematical Association
of America awarded her the Deborah and Franklin Tepper Haimo Award for
Distinguished College or University Teaching of Mathematics. In 2000, Professor
Hatcher was honored with the TCU Chancellor's Award for Distinguished Teaching
and was named the CASE Texas Professor of the Year.
Tilings in Higher Dimensions:
MAA Student Workshop Presented by Jeffrey Weeks
On Saturday, August 4, from 1:00 to 2:50 p.m. Dr. Jeffrey Weeks will present the MAA Student Workshop on the topic of Tilings in Higher Dimensions. Those who attended Dr. Weeks' invited address on the topic of Measuring the Universe at the winter AMS/MAA meetings in New Orleans (see page 3) are looking forward to another presentation that is not only highly educational but also highly entertaining.
Jeff Weeks goes by the unusual title of freelance mathematician. He
has an A.B. from Dartmouth College and a Ph.D. from Princeton University,
both in mathematics. His main interests are topology, geometry, education
and cosmology. After several years of teaching undergraduate mathematics,
he resigned to care full-time for his newborn son. When his son began school,
Jeff began doing mathematical research and software development for the
University of Minnesota's Geometry Center, designing and implementing research
software for creating and studying possible shapes for 3 dimensional space.
Currently a MacArthur Fellow, he splits his time between research and education.
His present research centers on a collaboration with cosmologists, with
whom he plans to test the topology of the universe using data to be provided
by NASA's Microwave Anisotropy Probe in 2002. His educational activities
have lead to a multimedia unit for middle schools on geometry and space.
The unit uses classroom activities, computer games, and video to let students
explore universes that are finite but have no boundaries. Jeff is the author
of the book The Shape of Space (Marcel Dekker, 1985), and the unit
Exploring the Shape of Space (Key Curriculum Press, 2001), and various
research and expository articles.
Call for Papers:
Fourteenth Annual MAA Undergraduate Student Paper
Session
Student papers have been a traditional part of the program for the MAA summer meeting, and this year is no exception. The Fourteenth MAA Undergraduate Student Paper Sessions will take place at the MAA Mathfest 2001 in Madison, Wisconsin, August 2 through 4.
Partial support for travel by students presenting papers will be available on a limited basis. Complete application details on submission procedures and applications for travel support will be published in the April issue of FOCUS. This information will also be available on the MAA home page at /students/students_index.html.
Students are advised to begin making plans now regarding participation. The deadline for student paper submissions is Friday, June 29, 2001.
Please direct all inquiries to Dr. Charles Diminnie via e-mail at charles.diminnie@angelo.edu
or by phone at (915) 942-2317, ext. 238.
Other Activities of Interest to Students at Mathfest 2001
The Student Hospitality Center will be open Thursday through Saturday, 9:00 a.m. - 5:00 p.m. Students and other Mathfest participants can meet here for informal conversation, refreshment, and mathematical diversions. The Hospitality Center also provides programs for the student paper sessions, packets for student presenters, and information on Mathfest activities of interest to students. Special information for students can be found on MAA Online at www.maa.org.
Abstracts From the Special Session on Mathematical Experiences for Students Outside of the Classroom;Joint Meetings, New Orleans, January 2001
Math Socialization: How to eat, drink, and be merry
while introducing mathematical reasoning, problem solving skills, and networking
Eva Culokova and Carol Marchetti, Rochester Institute of Technology
The Math/Statistics Club at Rochester Institute of Technology is an
informal collective of mathematics and statistics students and faculty.
Weekly meetings are known as "Coffee Hours" where coffee, tea, soda, and
cookies are provided. Each meeting is publicized by a flyer, which also
presents the "Puzzle of the Week." At the Coffee Hours, students socialize
with each other and with faculty and work on solving this week's puzzle.
Periodically, a faculty member will present an interesting mathematical
or statistical problem. Students also have the opportunity to present their
own projects or to learn about research and career prospects in their major
field. We believe that the social nature of these activities draws students
in. Building a network of friends and colleagues is vital to the success
of students. Seeing what more advanced students are working on helps them
to think about their future courses. Introducing them to faculty and their
interests provides an opportunity for independent study courses and research
at the undergraduate level.
Building a Successful Math Club
Tracii Friedman, Benedictine University
Three years ago, there were very few mathematics majors at my institution.
Thus, a primary goal of departmental strategic planning was identified:
increase the number of majors. The strategy included revitalizing the math
club and generating student research projects. In order to have a strong,
energetic program, it seemed essential to engage students outside of the
classroom environment, providing them with a view of mathematics that is
more than formulas, theorems, and number-crunching. In three years, the
math club has become an exciting and motivating component of the mathematics
department. We have also achieved much success with student research projects
and have included these projects as a regular math club activity. Generally,
the math club sponsors several annual events that include mathematics competitions,
outside speakers, and social events. There are biweekly and monthly events,
such as the Math Club Challenge, a problem posted in the student newspaper.
These events become familiar to the students and help to maintain momentum
throughout the year. Also, each year, the officers of the club aim to devise
at least one new, fun, and of course math-related event that helps to renew
student interest in the club's activities.
Bolygon Art: Experiences Forge Link Between Math and Art
Sue McMillen, Buffalo State College
In an early morning math enrichment program run from 1993 to 1996, 5^{th} and 6^{th} grade students were exposed to connections between math and art. The program began by viewing and discussing some of Picasso's paintings. Next the students participated in some discovery activities to determine a working definition of polygons. Picasso's works were then examined from the point of locating polygons within his paintings. Each student then drew five "polygon" art pictures of his or her own. Some students simply looked for polygons in their environment and reproduced them. Others drew abstract, Picasso-like drawings, merging polygons into larger shapes. Many of the students expressed surprise that geometry connected to art and to objects in the " real-world."
The students forged on by connecting coordinates to line segments that were used to construct polygons. They created simpler polygon pictures on a coordinate grid and then reproduced their artwork on graphing calculators. The students used a graphing calculator program to display each picture, drawn line segment-by-line segment on a projected display at a school science and math fair. They enjoyed the challenge of explaining to parents and peers how the mathematical artwork had been designed and constructed.
The students who participated are currently in their last two years
of high school or their first two years of college. Some are majoring in
math or still in high school and planning to major in math. They said the
program was one of their first experiences in "seeing" math used outside
of a math textbook. All were intrigued by the connections between art and
math and for many this was their first attempt to communicate mathematical
ideas to others. They credited the program with encouraging them to look
for links between math and other areas, as well as prompting an interest
in majoring in mathematics.
Needlework & Numbers: Patterns in Mathematics
Bonnie Burt, James Madison University
As an adult non-traditional learner, pursuing my Bachelors of Individualized Studies (BIS) via a portfolio process, I was required to take at least one semester of mathematics to fulfill my general education requirements. It had been over 28 years since I had participated in any type of mathematics course and it was a struggle to recall and apply methodologies that had long been forgotten (and unlearned). My professor, Dr. Fitzgerald, worked hard to find that connection in each of us that would unlock the mysteries of mathematics and apply it in our 'real life'. In other words, to move from just concepts to be memorized and recited to owning and understanding them in a tangible way. Dr. Fitzgerald approached me at the end of the semester with a unique concept: To develop a quilt that incorporated mathematical principles and pattern.
As a quilter, this challenge sparked my interest and I took on this
assignment with enthusiasm. I selected the golden rectangle -- and its
subsequent diminishing rectangles within a rectangle pattern -- as the
foundation block. The quilting highlights the spirals that result from
connecting each rectangle corner to corner, in this case with thread. I
further explored this phenomenon in nature and our every day life.
Undergraduate Organization of High School Mathematics Competition
Debbie Czarneski, Mount Mercy College
On October 20, 2000, Mount Mercy College hosted its third annual high
school mathematics competition. Our competition has participants compete
in modeling, speed, accuracy, depth, story problem, and non-calculator
activities. The students of the Mount Mercy Mathematics Club play crucial
role in almost every aspect of the competitions including organization,
proctoring, grading tests and modeling papers, and computerizing our score
reports. As student coordinator of all three competitions, I have experienced
the initial organization and planning of a student run competition as well
as the implementation in successive years. Development of our competition
in the areas of finance, participation, and scheduling will be detailed.
I shall also discuss some of the problems we have encountered, especially
those in our initial competition, as well as the adjustments that we have
made to improve the competition each year.
An R. L. Moore Discovery Learning Experience in Real Analysis over Pizza
Anahita Rafiee, Stephen Stull, and Nick Pepers, Augusta State University
(Sponsor: Dr. C. Stallmann)
R. L. Moore (1882-1974) at the University of Texas, produced what is
regarded by many as the "most distinguished group of mathematicians in
the United States to have been taught by the same person." His technique,
called the "Moore Method" is sometimes referred to as "discovery learning."
Inspired by a presentation at the DC meetings last year we managed to connect
with an actual student of R. L. Moore's in our area, Dr. William Mahavier.
After doing some research and watching a few videos, the ASU MAA student
chapter had Dr. Mahavier as a speaker on campus. Using Dr. Mahavier's notes
and suggestions, Dr. Cornelius Stallmann started a small discovery learning
experience in Real Analysis over pizza for interested students from our
MAA student chapter. As a side note, this "Outside the Classroom Experience"
has actually spawned a class. Dr. Stallmann will continue this project
in a special topics class at Augusta State, Math 2950, during the spring
semester of 2001.
Sine on the Dotted Line: The Carthage College Journal of Undergraduate Mathematics
Aaron K. Trautwein, Carthage College
The students and faculty at Carthage College created their own undergraduate
mathematics journal, "Sine on the Dotted Line," seven years ago. Since
that time, eight issues have been published. This presentation gives the
history of the journal, how the journal has affected changes and additions
to the Mathematics Department curriculum, and the process by which each
issue is published. In addition, examples of articles appearing in the
journal will be given. The talk will conclude with a description of how
the journal has enhanced mathematics learning outside the classroom at
Carthage and an examination of some of the successes and problems we have
encountered.
Higher Math: The Venus Transit Project
Thomas Kelley, Henry Ford Community College
This is a preliminary call for volunteers to put together a project for student chapters and/or math clubs. A "Transit" of Venus occurs when the planet Venus comes between the earth and the sun at the time when all three are in the same plane. Because the elliptical orbits of the Earth and Venus lie in different planes this means we have a pair of transits separated by 8 years occurring about every 120 years. The next transit is to occur in June of 2004, followed by one in December of 2012.
The MAA would have a Venus Transit website linked to its Student Chapter site. This site will have the algorithm to compute the AU (Astronomical Unit) based on observations taken at many locations around the world. Student Chapters in regions with good viewing prospects for the transit could be partners for those in areas where the transit cannot be seen in its entirety. Information to be collected for the transit consists of latitude and longitude (GPS will be of great help here) and the local time of entry and egress of Venus onto the sun's disk. Sites would report their data at the central location and perform computations either locally or on the website using data from site(s) that will give a long "baseline" for the calculations.
Why do we have to start now if the next Transit of Venus isn't going
to happen until June, 2004? There's a lot to get organized and set up so
this will work. The math is doable, but nontrivial. Finally, in the spirit
of the history of the project, explorers for the 1761 transit had to start
out more than a year before in order to reach remote locations like Siberia,
Madagascar, and Northern Hudson Bay, Canada.
Abstracts From the Special Session on Mathematical Experiences for Students Outside of the Classroom;
Joint Meetings, Washington, DC, January 2000
History as an Ice-Breaker
Jean Chan, Sonoma State University
This is an ice-breaker game for mathematics students. The purpose is for players to learn some facts about mathematicians as well as some interesting facts about other students. For definiteness, assume this game will be played by 30 students.
Prepare two sets of 15 name tags for different mathematicians and two
sets of 15 small slips of paper with facts about the 15 mathematicians.
Prepare 30 forms for the treasure hunt. Each forms lists all 15 facts.
To begin the game, pass out pencils and name tags to everyone, and give
each person a slip of fact to learn and hide. Now each player must go around
asking others in order to find the right mathematician's name to match
each fact and some interesting fact about the student wearing the mathematician's
name tag. The first person to finish the form wins. This game is much more
fun to play than to describe.
Problem Solving Groups
Jim Vandergriff, Austin Peay State University
We will present our strategy for this valuable extracurricular activity, including motivation, problem selection, problem solving techniques, and solution presentation.
Motivation applies to the advisor as well as to the students. I will discuss my motivation and activities that keep me motivated. For the students, we present in detail the reasons why they should be involved. After motivation, selection of problems is the next critical step. A list of journals used by APSU will be discussed as well as the criteria for selection of problems.
We will provide techniques to help students to solve problems as well
as software that will enhance their abilities. Finally, the presentation
of the solution is as important as the solution. The astute student learns
valuable writing and presentation techniques. Applicable software will
be discussed.
Enhancing the Study of Mathematics
Alexandra Kurepa, North Carolina A&T State University
The Math Department at North Carolina A&T State University has developed a rich tradition of organizing outside-the-classroom activities that promote mathematics, celebrate the beauty and diversity of mathematics, and encourage students to pursue careers in mathematics. The department organizes the very successful NCA&T Lecture Series in Mathematics, now in its eight year, Math Awareness Day, now in its 4^{th} year and The NCA&T Sonia Kovalevskaya Day in its third year. The NCA&T MAA Student Chapter is actively involved in these activities.
The North Carolina A&T State University Mathematics Lecture Series
brings distinguished mathematicians to the A&T campus to lecture on
their work. The students have the opportunity to interact with the guest
mathematicians making contacts that are helpful in the furtherance of their
education or research projects as well as in finding internships and employment.
The Lecture Series is sometimes coordinated with other events in the Department
such as the Sonia Kovalevskaya Day, which focuses on activities that promote
mathematics and encourage more women to study mathematics, as well as the
Mathematics Awareness Day, which meets the needs of both the graduate and
the undergraduate students. A student mini conference held during the Math
Awareness Month in April provides an opportunity for graduate students
and some undergraduate students to make professional presentations on their
research in a friendly and familiar environment. Graduate students from
nearby universities are invited to participate and the best student presentation
is awarded a certificate. Up to 150 undergraduate students participate
in the afternoon Differentiation and Integration contest which generates
a lot of interest even from other Colleges. The day concludes with the
awarding of prizes to students demonstrating outstanding skills in these
areas.
Nurturing a Community of Students at a Large University
Paul Fishback, Grand Valley State University
The Department of Mathematics and Statistics at Grand Valley State University
(GVSU) offers many opportunities for our students to become involved in
mathematical activities beyond the classroom. The Mathematics and Statistics
Club/Student MAA Chapter activities over the past few years have included
inviting career speakers, establishing problem solving groups, assisting
the department in its interviewing of job applicants, advising the department
on issues of student concern, hosting social activities, and organizing
the Michigan Undergraduate Mathematics Conference. In addition to the club,
the department actively promotes collaborative research between students
and faculty. Some of these projects have focused on research problems in
pure mathematics and have led to a recent NSF-REU grant. Others address
problems in statistical consulting for a variety of clients in the region.
These types of activities have done much to "fertilize" an undergraduate
mathematics community within our department, a community that flourishes
despite the large size of our institution (over 17,000 students). Important
factors that make the creation of such an environment possible include
the institutional commitment to teaching excellence, service, and scholarship
as well as significant contributions made by a large number of motivated
faculty.
Into the Workforce: College Students Help Present Math-Related Career Possibilities to Eighth-Grade Girls
Maria Hernandez, Math Teacher at NC School of Science & Math, Math Mentor; Natalie Murray, Meredith College undergraduate, Member of Sonya Kovalevsky Day Student Team
This presentation describes The Math Mentoring Program and one of the program's highlights: Sonya Kovalevsky Day. Sonya Kovalevsky Day is the day-long career conference held at Meredith College for participants in the Math Mentoring Program in the Wake County public schools.
The Math Mentoring Program aims to encourage young women, who have an interest in math, to "stay on the math path." Program objectives are to make students more aware of mathematics-related careers, and to increase students' appreciation for, and self-confidence in, mathematics. The Math Mentoring Program is a joint project of the NC region of the Women & Mathematics Network, Meredith College, NC Central University, and the Durham and Wake county public school systems. Begun in 1993, it annually involves approximately 160 eighth-grade girls, 60 mentors, and a Coordinating Team of twelve. The Program receives corporate funding from GE Capital Mortgage Corporation, GlaxoWellcome Inc., and Reichhold, Inc.
The Math Mentors are volunteer female professionals whose jobs are in the fields of mathematics, science or technology. Each math mentor is linked up with three girls from the same school. Through monthly activities from January through May, the students learn about their mentor's job, career, and interests. Mentors become role models as they interact with their student group. Students and mentors participate in a variety of field trips to places of math and science interest, work on projects, discuss future coursework and enrichment programs, etc.
Sonya Kovalevsky Math and Computer Science Career Awareness Day consists of workshops, mentor panels, lunch, a math competition and T-shirts. It is organized and implemented by a team of Meredith College undergraduate students who are majoring in mathematics or mathematics-related subjects.
For the college students, SK Day has several positive outcomes: (1)
Team members get to hone their communication and organization skills. (2)
They get to know professional women who have mathematics-related jobs.
(3) Team members who are planning to teach report that they especially
value the experience with adolescent girls in this out-of-the-classroom
event.
Math Experiences Outside the Classroom for University of Houston Students
Ken Oberhoff, University of Houston
This talk will describe a number of activities of our students including
a brief discussion of some of the over 200 Senior Research Projects completed
by our students in business, industry and government including some with
NASA-JSC and the University of Texas Medical Center. In addition, a large
number of our students are engaged in faculty/student grants ranging from
tutoring to large-scale research projects. For example, one grant supports
approximately ten of our students in research projects every semester.
In addition, our math and computer clubs sponsor high school math and computer
programming contests and also a number of social events. This talk will
describe these and other student activities.
Ins and Outs of Math Celebrations
Dora Ahmadi, Morehead State University
This paper will share experiences gathered in celebrating Mathematics Awareness Week through several years. In particular the following issues will be addressed:
- Getting started,
- Seeking financial resources,
- Getting faculty members and students involved,
- Reaching out to high school, middle school, and elementary school
students,
- Reaching out to businesses and city officials, and
- Highlights of activities through the years such as problem solving
contests at the university level, a high school T-shirt contest, math fairs,
math carnivals, and other student oriented activities.
The Scarecrow Conjecture Activity
James Yick, President of the Euclidean Society
(MAA Student Chapter at Augusta State University)
In the original movie version of The Wizard of Oz, when the wizard gives the scarecrow a diploma, a "Doctorate in Thinkology" or Th.D, to show the effect of his newly acquired degree, the scarecrow rattles off something that sounds somewhat like the Pythagorean Theorem but is not. He states, "The sum of the square roots of any two sides of an iscoceles triangle is equal to the square root of the remaining side." We will call this the Scarecrow Conjecture. For a disproof by counterexample, take an equilateral triangle with all sides of length 1. Since sqrt[1] + sqrt[1] does not equal sqrt[1], the conjecture is false.
The Crow Theorem: The sum of the square roots of any two sides of an isosceles triangle is not equal to the square root of the remaining side.
Proof by Contradiction: Consider any isosceles triangle with sides of lengths a, a, and b with 2a>b>0. Assume that the sum of the square roots of two sides of the triangle equals the square root of the remaining side. We consider two cases:
Case (i): sqrt[b] = sqrt[a] + sqrt[a]
Sqrt[b] = 2sqrt[a]
b = 4a>2a>b
b>b is false.
Case(ii): sqrt[a] = sqrt[a] + sqrt[b]
0 = sqt[b]
0 = b, a contradiction.
This experience can include a discussion about the symbolic nature of the scarecrow as representing uneducated farmers and why the scarecrow's conjecture may have been deliberately false.
Joint Mathematics Meetings
San Diego
January 6 - 9, 2002
SEE YOU THERE!
Contact Information
How to Reach the MAA
For Membership Information, Subscriptions, and Publications orders contact:
The MAA Service Center
P.O. Box 9112
Washington, DC 20090-1622
800-331-1622 or (301) 617-9415
(301) 206-9789-FAX
For the MAA Headquarters:
The Mathematical Association of America
1529 Eighteenth Street, NW
Washington, DC 20036-1385
800-741-9415 or (202) 387-5200
(202) 265-2384-FAX
To Contact the
Chapter News Editor
Suggestions, concerns, and/or contributions of articles for this newsletter may be sent to:
James P. Marshall
Illinois College
Department of Mathematics
1101 W. College Ave.
Jacksonville, IL 62650
(217) 245-3432
FAX: (217) 245-3034
jmarshal@hilltop.ic.edu
May the MATH be with you!