Off on a Tangent
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A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
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This
week's colloquium
speaker is a GVSU student
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Title:
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A Sieve for Betweenness of Compact Sets
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Speaker:
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Geoff Patterson, GVSU |
Time:
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Thursday,
March 26 at 4:00 p.m.
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Place:
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VWF
104
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Abstract: The Hausdorff metric measures how far two
compact non-empty subsets of a metric space are from each other.
We can define what it means for a set to be between to other sets,
similar to the idea of betweenness in the standard Euclidean
metric.
Previous research has shown that for two sets A and B it is possible to have multiple
distinct sets at the same location between A and B. It turns out that this
number of distinct sets at a given location is well-defined for any
location between the two sets. It has also been shown that we can
find sets A and B with k sets at any location between A and B for k between 1 and 18. However,
it has been proven that is impossible to have A and B with 19 sets at any location
between them. This result is surprising and motivates further
investigation into the calculation of the number of sets at any
location between two sets A
and B.
A natural question to ask is what other numbers may be unobtainable,
like 19. My senior thesis project was to develop a sieve which
can search for such numbers.
Please join us for refreshments
in VWF 222 at 3:45 p.m.
Next
week's colloquium features WMU professor
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Title:
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Beware of
Geeks Bearing Grifts
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Speaker:
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Prof. Allen Schwenk, Western Michigan
University |
Time:
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Thursday,
April 2 at 4:00 p.m.
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| Place: |
VWF
104
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Abstract: What’s a
grift? It is one of those games you see on the carnival midway
that is (perhaps) not quite dishonest, but is certainly
misleading. If I show you three nonstandard dice with a strange
selection of numbers, do you think you could choose the one with the
best chance of winning? Are you sure? We shall
construct nonstandard sets of dice that not only possess the curious
property of “nontransitivity,” but also display the paradox of
“perverse reversal”. We continue to investigate unexpected
appearances of nontransitivity involving coin tossing and the game of
Bingo. We also observe the paradox of “waiting time reversal”.
Today is
the last day to sign up for the LMMC
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| Contest Date: |
Saturday,
April 4 |
Location:
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Albion
College
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How to Register:
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Sign up on
the sheet on Prof. Cinzori's Door (VWF 216) or email him at
cinzori@hope.edu
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| Registration Deadline: |
Wednesday,
March 25 |
The 33rd Annual Lower Michigan
Mathematics Competition will be held
at Albion College this year on Saturday, April 4. Students
from colleges and universities in Michigan will gather there to
challenge themselves on 10 interesting problems, working together in
teams of up to three people. The competition runs from 9:30 a.m. to
12:30 p.m. After the problem session in the morning, there will be a
break for lunch followed by a solutions session in the afternoon.
Sign-up information is shown
above. You may register as a team (of two or three) or
individually (and you will be placed on a team). Hope has a
history of strong showings at
the LMMC, including several
championships, and we'd like to regain the title this year and bring
the Klein Bottle Trophy back to Hope!
The
Problem of the Fortnight
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The
Problem of the Fortnight has two parts this time:
1. Which of the five numbers 2007, 2008, 2009, 2010, and 2011 has
the largest number of
factors, and which one has the fewest
number of factors?
2. Determine the total
number of factors for the number
(2007)(2008)(2009)(2010)(2011).
For example, 21 has 4 factors (1, 3, 7, 21) and 20 has 6 factors (1, 2,
4, 5, 10, 20).
Write
your solution (not just the answer!) on the back of two NCAA Final Four
tickets and drop
it off at Dr.
Pearson's office (VWF 212) by noon
on Friday, April 3.
As always, be sure
to write your name, the name(s) of your
professor(s), and your math class(es) on your solution (e.g. Factor
Fiction, Professor Count M. Up).
Good luck, and have
fun!
Problem
Solvers of the Fortnight
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The last problem of the fortnight was:
An
n x n matrix is called a
Latin square
if each of the integers 1, 2,
..., n occurs exactly once
in
each row and each column. Find the
number of distinct 4 x 4 Latin squares.
Congratulations
to the following problem solvers of the fortnight, who determined that
there are 576 distinct 4 x 4 Latin squares: Brian McLellan, David
Todd, Dan Waldo, Eric O'Brien, Andrea Eddy, Dale Schipper, Luke
Hoogeveen, Bruce Kraay, Cortney Kimmel, John Bruggers, Joshua Borycz,
Amy Speelman, Kelsey Bos, Kelly Shugart, Nathan Erber, Andrea Toren,
and Kyle Gibson. Kyle's elegant solution is posted on the
bulletin board.
Problems,
Puzzles, and Pizza 2009
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Lots of fun was had at a recent mathematics department
gathering. Students wandered from table to table to play games
and work puzzles of various sorts. The students shown in the
foreground here are playing the Pentomino Race Game. Other
students are playing Set, Jinga, Blackjack, and Suduko. Students
also had the opportunity to try their hand at Origami and work with
bubbles. Fabulous prizes were given out and lots of pizza was
eaten.
Even
if you're on the right track, you'll get run over if you just sit there.
--- Will Rogers
The last problem of the fortnight was: