Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
   March 5, 2008 Vol. 6, No. 10  
http://www.math.hope.edu/newsletter.html


How to Build a Better Slide

Title:
 Building a Better Slide or “The Brachistochrone Problem”
Speaker:
 Prof. Tim Pennings, Hope Mathematics Dept.
Time:
 Thursday, March 6 at 4:00 p.m.
Place:
 VWF 238

  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. 


Lower Michigan Mathematics Competition will be held soon

Contest Date: Saturday, April 5
Location:
Lawrence Technological University in Southfield, Michigan
How to Register:
 Sign up on the sheet on Prof. Edwards Door (VWF 218) or email her at sedwards@hope.edu
Registration Deadline: Wednesday,  March 26

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, March 26.

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

A 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).  Be sure 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!
Problem Solvers of the Fortnight

The previous problem of the fortnight was to solve the equation
(ln x)2 - 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!
Special Challenge Problem from Ryan

In the 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 as 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
The 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 Thursday.)
Greetings from (another) Ryan in Budapest

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:
Hey folks!  Math classes are in full swing and the homework keeps on coming.  Last weekend I was able to find the time to go with some friends to Eger, a small town in Hungary in the middle of the wine country.  That weekend we experienced the most beautiful 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 really sweet castle in Eger that was just 2 blocks from where our hostel was.  We 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 still 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 some of the crippled people I see by the tram most days.  I wish there was more I could do, but not being able to speak Hungarian puts a real barrier between most people and me.
 
Egeszegedra,
Ryan 


One is the loneliest number...
~ Harry Nilsson (1941-1994)
Off on a Tangent