|OFF ON A TANGENT
|A Fortnightly Electronic Newsletter from the Hope
College Department of Mathematics
colloquium to be on the Poincaré Conjecture
Prof. Gerard Venema of Calvin College will be here tomorrow to
speak on "Recent Developments Regarding the Shapes of
- Thursday, October 6 at 4:00 p.m.
- 104 VWF
A space that at small scales resembles Euclidean 3-space is called a
3-dimensional manifold. Such spaces can have complicated and
interesting large-scale structure. Recent breakthrough work by the
Russian mathematician Grisha Perelman appears to have resolved one of
the major questions regarding 3-manifolds — the century-old
Poincaré Conjecture. Perelman's solution is most surprising in
that he establishes a much more sweeping result, known as Thurston's
Geometrization Conjecture, that relate the geometry and topology of
In this talk Prof. Venema will attempt to explain what Perelman has
proved about 3-manifolds by analogy with 2-dimensional results. In
particular he will explain the difference between the topology and
geometry of a space and what it means for a space to have a natural
geometry of constant curvature. If time permits he will conclude with
some speculation about implications for the shape of the physical
Don't forget that tea time will precede the colloquium at 3:30 p.m. in
scheduled for next week
You all know that next week Wednesday (when you return from fall
break) is declared to be a Monday by the registrar's office. The
mathematics department (for colloquium purposes only) is declaring next
week Thursday to be a Tuesday. Since we have colloquia on
Thursdays, and there will not be a Thursday next week, we will not have
a colloquium. We thought this method of changing days around
would be the most logical for all. So remember next week will go
Monday, Tuesday, Monday, Tuesday, Friday. (I think the SAC movie
next week should be Groundhog Day!) We would like to change
Friday to a Saturday, but that is out of our hands.
Just to make things a bit more difficult. Next week October 12 is
Columbus Day. However, somebody at the Post Office, I think,
likes to have Monday holidays. This means that next week Monday
(which is a Monday) will be October 12. So the dates for next
week Monday through Friday go 12th-11th-10th-13th-14th. Got
Let's play Mathematical Jeopardy!
mathematics department will conduct a Mathematical Jeopardy competition
on Thursday, October 20 at 4:00 p.m. (tentatively in VWF 102). Entry
is free and there will be prizes for the winning team! Sign up on
Professor Stephenson’s door (VWF 210) by Monday, October 17 or email
him at email@example.com if you would like to be a contestant.
Here are some of the particulars.
- You may sign up as a complete team (4 students or
less). Include the names of all team members and a team
name. (You must make up a team name, or we will choose one for
- You may also sign up individually, and we will put you on a team.
- This contest is open to everyone – students at all
mathematical levels are encouraged to participate. Questions will
be chosen from a broad range of topics, including films and history.
- Refreshments will be served following the competition.
Statistics Career Day next month at GVSU
On October 14 the Southwest Michigan Chapter of the American
Statistical Association (ASA) and the Grand Valley State University
Department of Statistics will present a Statistics
Career Day on their Allendale Campus. Exhibits on employment
in statistics from governmental agencies and private industry will be
available as well as those from graduate schools. There will also
be a number of talks given about employment as well as a keynote
address from ASA president Fritz J. Scheuren.
For more information about this event you may contact either Prof.
Bekmetjev or Prof. Tintle. (Information can also be found at
Statistics Career Day link in the preceding paragraph.)
It is time to think about
competing in the fall mathematics competitions
Two mathematics competitions that take place each fall at Hope College
are the MATH Challenge and the Putnam Exam. Information about
each of these follows.
The MATH Challenge
The 2005 Michigan Autumn Take Home Challenge (or MATH Challenge) will
take place on the morning of Saturday, October 29 this year.
Teams of two or three students take a three-hour exam consisting of ten
interesting problems dealing with topics and concepts found in the
undergraduate mathematics curriculum. Each team takes the exam at
their home campus under the supervision of a faculty advisor.
The department pays the registration fee for each team and will provide
lunch to participants afterwards. The sign-up deadline is
Wednesday, October 12, 2005 at 5:00 p.m. Interested students can
sign up by sending Prof. Cinzori an email at firstname.lastname@example.org or by
signing up on the list on his office door (VWF 216).
A group of students may sign up as a team. Individual students
are also encourage to sign up; they will be assigned to a team on the
day of the competition. For more information about this
competition and to view copies of old exams visit http://www.mcs.alma.edu/mathchallenge/.
The Putnam Exam
The William Lowell Putnam Mathematical Competition, administered
by the Mathematical Association of America, is the most prestigious
mathematical competition for undergraduates in the nation. If
you are interested in taking the 66th Annual Wm. Lowell Putnam Exam,
you must sign up by this Friday, Oct. 7 with Prof.
Stoughton. The date of the exam
is Saturday, December 3, 2005. There is both a morning and an afternoon
session of this exam; lunch will be provided by the mathematics
department during the break. For more information about the
Putnam Exam visit http://math.scu.edu/putnam/.
(As of today, this official Putnam site hasn't been updated since last
year, but still gives some useful information.) For
questions and solutions from past exams visit http://www.kalva.demon.co.uk/putnam.html.
The Michigan Undergraduate
Mathematics Conference will be held this month
The Department of Mathematics at the University of Michigan at Flint
will be hosting the eighth annual Michigan Undergraduate Mathematics
Conference (MUMC) on Saturday, October 22, 2005. Hope College
will be taking a group of students and faculty. They will leave
early in the day and return in the evening.
Undergraduate students will be giving 20-minute oral presentations
on many areas of mathematics, statistics or related discipline. Such
areas include undergraduate research projects, interesting class
projects, history of mathematics, or expository talks on interesting
mathematics. Students are also encourage just to attend as there
will be presentations on careers in mathematics, information about
mathematics graduate programs and REU programs.
For students interested in attending need to sign up with Prof.
Darin Stephenson by October 12 (he has a sign-up sheet outside his
office door, VWF 210). Visit the MUMC web page at http://www.umflint.edu/departments/math/mumc2005/index.html
for more information about the conference.
Problem of the Fortnight
about big numbers. . . .
Find the smallest N, or show
that none exists, for which the decimal
ends in exactly
Write your solution on the back of two 2005 American League
Championship Series tickets, or on the back of a $2005 bill, and drop
it in the Problem of the Fortnight slot outside Dr. Pearson's office
(VWF 212) by 3:00 Friday, October 14.
Problem Solvers of the Fortnight
We received many interesting solutions to the problem in the last
issue, including two written on styrofoam egg cartons. Only nine
people, though, found the best strategy. Congratulations to
Allen, Benjamin Crumpler, James Daly, Erica Dickinson, Derek Duncan,
Nathan Makowski, Jeff Mastin, Jon Moerdyk, and Megan Patnott for
handling this egg problem with such delicate care and hatching elegant
The least number of drops that are needed to determine with certainty,
even in the worst case scenario, is eight. The idea is to keep
total number of drops the same. First drop the egg from the
floor. If it breaks, the only thing to do is go to floor one and
proceed upward; in the worst case, you need to go to the seventh floor,
in which case eight drops were needed to determine this. If,
the egg survives a drop from the eighth floor, we want to keep the
total number of drops the same, and so having already made one drop, we
can only go up seven floors. So drop it from the 15th
floor. If it
doesn't survive, go to the ninth floor and proceed upwards; in the
worst case, you need to go to the 14th floor, in which case a total of
eight drops (one from floor eight and seven from floors 9 - 14) were
required. Proceed to floors 21, 26, 30, 33, and 35, as
an egg dropped from the 35th floor survives, we will have made 7 drops
already, and a final drop from the 36th floor will determine exactly
where the egg breaks.
The answer to this problem is beautiful. It involves triangular
numbers, which are numbers obtained by adding all positive integers
less than or equal to a given integer. For example, 10 is a
number: 10 = 1 + 2 + 3 + 4. They are called triangular numbers
the integers involved in the sum may be arranged to form a
For example, the integers 1, 2, 3, 4 may be arranged like pins on a
bowling alley to form a triangle.
For more on triangular numbers, visit http://mathworld.wolfram.com/TriangularNumber.html.
So . . . what can I do with a
degree in mathematics?
Bush nominated Harriet Miers to fill the vacancy on the Supreme Court
left by the retirement of Sandra Day O'Connor. In the newsroom at
"Off on a Tangent" our ears perked up when we heard the radio news
report that she had obtained a B.S. in mathematics from SMU. So
if you're thinking about majoring or minoring in mathematics but are
worried that your choice of studies may not further your career goal of
being associate justice of the Supreme Court of the United States, you
need not worry. All
joking aside, many law schools look favorably on applicants who majored
in mathematics because of their ability to construct tightly reasoned,
Political pundits have been speculating that diversity of the Court
would be a primary consideration for President Bush in choosing a
nominee. The current justices, along with their majors and
undergraduate institutions, are:
If sworn in, Miers would be the only mathematics major on the court,
though not the only one in its history. Justice Harry Blackmun,
an associate justice on the Supreme Court from 1970-1994, was a also
- Sandra Day O'Connor – Economics, Stanford
- John Paul Stevens - English Literature, University of Chicago
- Stephen Breyer - Philosophy, Stanford
- Ruth Bader Ginsburg - Government, Cornell
- Anthony M. Kennedy - Political Science, Stanford
- Antonin Scalia - History, Georgetown
- Clarence Thomas - English, Holy Cross
- David Souter - Philosophy, Harvard
- John Roberts - History, Harvard
|Got a Math Question?
Ask Elvis ...
... email him at email@example.com
Did you hear that Akira Haraguchi, from Japan, recited the first 83,431
digits of pi from memory this past summer? He finished this
astonishing feat in 13 hours. He did, however, have some trouble
along the way. He lost his place after reciting the first 16,000
digits and was forced to start over. (Don't you hate it when that
happens?) After starting over he managed to break the old record
of 42,195 digits set by a 21-year-old Japanese student in
I don't know about you, but I don't like to spend too much time
memorizing digits. I do, however, have committed to memory the
83,431 different food and non food odors. For example, I can
detect the subtle differences between the smell of beet soup and moldy
shoe leather. I find this to be a much more rewarding talent.
I do have one letter to answer today. Don't forget to keep those
questions coming in. It is always nice to get non-spam
I have heard (from slashdot.com)
that a new way of doing
trigonometry has been developed. This new way doesn't involve using any
classical trigonometric functions. If you follow this link, you will find a PDF
of the first chapter of the book that it is revealed in. It seems
fairly simple and the author, Dr. Norman Wildberger, of the South Wales
University in Australia, does a good job of explaining it. However I
was wondering if you could share your thoughts on this new technique.
Best Itches (uh...I mean wishes),
You know what they say. It is hard to teach an old dog new
tricks. That is the way I feel about rational trigonometry.
I know all the angles on classical trigonometry. I know the
difference between a cosine and a coconut, as well as the difference
between a tangent and a tangerine. Therefore, I am comfortable
with the old ways. However, you young whippersnappers are
certainly welcomed to explore new ways of doing mathematics. For
that is the way new discoveries are made!
right to swing my fist ends where the other man's nose begins.
Wendell Holmes, Jr.,
Associate Justice of the U.S. Supreme Court from 1902-1932