|Off on a Tangent
|A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
Build a Better Slide
|Building a Better Slide or “The
Pennings, Hope Mathematics Dept.
March 6 at
Abstract: A solution to the
brachistochrone problem was developed by some of the greatest minds in
mathematical history including: Bernoulli, Euler, Leibnitz, L’Hospital,
and Newton. In this talk (another great mind?) Pennings will show,
using partial derivatives from Math 232, how to build a slide that one
can slide “down” in minimum time. In the process, we find a
general formula for finding extreme of many natural phenomena.
Michigan Mathematics Competition will be held soon
Technological University in Southfield, Michigan
|How to Register:
|Sign up on
the sheet on Prof. Edwards Door (VWF 218) or email her at
The 32nd Annual Lower Michigan
Mathematics Competition will be held
at Lawrence Tech this year on Saturday, April 5. 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.
Registration is free and students in Math 131 and up are encouraged to
participate. Interested students may sign up individually or in teams.
The deadline for registering is Wednesday,
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!
Problem of the Fortnight
probability density function on [a,b] is a positive function where the
area under the curve over the interval [a,b]
is 1. The median, a
common measure of the center of a probability density function, is the
value m in [a,b] where half
the area under the probability density function lies to the left of m and half lies to the right of m.
The problem this fortnight is: Find positive numbers b and k such that f(x)
= kx3 is a
probability density function on [0,b]
with a median of 3.
Write your solution on a piece of paper that is cut to resemble your
probability density function, and drop it
by Dr. Pearson's office (VWF 212) by noon
on Thursday, March 13 (the day
before Spring Break).
to write your name, the name(s) of your
professor(s), and your math class(es) on your solution (e.g. Marge N.
Averra, Prof. N. T. Grate, Math 172). Good luck, and have fun!
Solvers of the Fortnight
previous problem of the fortnight was to solve
- 2.5(ln x)(ln(4x-5)) + (ln(4x-5))2 = 0
where x and all expressions
in the equation are real.
The only real solution to this equation is x = 25/16. A detailed
solution of the problem is posted on the math bulletin board, and you
can check it out there!
Congratulations to: Zach Mitchell,
Andrea Eddy, Adam Plaunt, Kelsey Browne, Ben Herrman, Josh Kinder,
Shirley Bradley, Keith Mulder, Kaitlyn Kopke, Carleen Dykstra, Dan
Waldo, Eric O'Brien, Kristian Cunningham, Matt Smith, Joel Blok, David
Boothe, Chris Jordan, Mark Gilmore, Mark Panaggio, James Daly, Chris
Hall, Luke Wendt, Thao Le, Valerie Winton, Terra Fox, Megan Pearson,
Kimberly Klask, Hannah Kasperson, Stephanie Pasek, Chelsea Miedema, and
Ashley Gruenberg. Thanks especially to those who attached a stick
to their solution!
Challenge Problem from Ryan
last issue, we informed our gentle readers about the following problem
that appeared in neatly written cursive
handwriting outside Dr. Stephenson's door, and the response was
terrific! We've received many solutions, but we'll put it to you
a special challenge problem again, in the hopes that many more
solutions will be forthcoming.
Solve for x:
x(9/5) + 6/x = 78/10
problem was posed by Dr. Stephenson's son Ryan, who's a fifth
grader. Although this special challenge problem will not count as a Problem of the
Fortnight, we encourage you to drop a solution in the envelope Ryan has
created on the bulletin board outside his dad's office. Ryan will
choose a winner randomly from the correct solutions he receives.
We at Off on a Tangent will keep you posted about this special
challenge problem contest and announce the winner when Ryan selects
one. (Note: There isn't a due date on the problem, so we
encourage you to submit your solution soon! Preliminary reports
indicate that Ryan would like to conclude his special challenge problem
before our Spring Break, so please get your solutions in before next
Ryan Johnson, a junior math major at Hope,
is spending a semester studying mathematics in Budapest, Hungary, as a
part of the Budapest Semesters Program in Mathematics. The crack
staff of America's preeminent fortnightly mathematics department
electronic newsletter, Off on a
Tangent, wish they had tracked Ryan down on the streets of
Budapest, but instead he just emailed us. Here's a little of what
he had to say about his experiences studying math in Budapest:
from (another) Ryan in Budapest
Math classes are in full swing and the
homework keeps on coming. Last weekend I was able to find the
go with some friends to Eger, a small town in Hungary in the middle of
the wine country. That weekend we experienced the most
weather since coming to Hungary. The sun was shining and the
temperature was somewhere in between sweatshirt and long sleeve T-shirt
range. We also saw a beautiful cathedral while we were
there. There is a
castle in Eger that was just 2 blocks from where our hostel was.
also imitated a few statues and stuff which was a lot of fun (see
picture at above).
One thing I find
hard to get used to in this city are the homeless
people. I mentioned this to one or two of you already, but it's
on my mind. Hungary's economy is much better than some of its
neighbors like Romania, but it still has a while to go before the EU
will let it be apart of Euro currency. I give spare change to
the crippled people I see by the tram most days. I wish there was
I could do, but not being able to speak Hungarian puts a real barrier
between most people and me.
One is the loneliest number...
~ Harry Nilsson (1941-1994)