Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  April 15, 2011 Vol. 9, No. 14
http://www.math.hope.edu/newsletter.html


Two more mathematics colloquia set for this semester

There are two remaining mathematics colloquia scheduled for this semester.  Matt Boelkins will speak on Tuesday, April 19 at 11:00 a.m. (note the unusual time) and Melinda Koelling will speak on Tuesday, April 26 at 4:00 p.m.  Both talks will be presented in VanderWerf 104.  The title for Prof. Koelling's talk will be announced later.

Title: How Seashells Grow:  A Spiral Story
Speaker: Matt Boelkins, Grand Valley State University
Time:  Tuesday, April 19 at 11 a.m.
Place:  VWF 104

Abstract: Spirals are evident in many natural phenomena:  seed patterns in flowers, satellite photos of hurricanes, images of galaxies in space, and a wide range of seashells. How can mathematical models be developed to represent the shapes and patterns we observe in seashells?  In this talk we’ll explore how parametric curves in two- and three-dimensions, parametric surfaces, and a few other fundamental ideas from multivariable calculus combine to produce two different models that generate beautiful, accurate images of seashells through the computer algebra systems Maple and Mathematica.


Speaker: Melinda Koelling, Western Michigan University
Time:  Tuesday, April 26 at 4 p.m.
Place:  VWF 104

 

Integration Confrontation


The Integration Confrontation will be Wednesday April 20th at 3 PM in VZN 297.  Teams of 1-3 students will compete solving challenging
integrals.  Fabulous prizes for the winners.  Please sign up by by 1:00 PM on Tuesday April 19th  on Professor Edwards' door.  You may
sign up as a team or we will place individuals on teams if they desire.  Participation in this event is worth one colloquium credit and the students should be in Calculus II or beyond.


Summer research students receive recognition in statistics contest


Scott Powers of the University of North Carolina and Alexander Luedtke of Brown University worked with professors Tintle and Bekmetjev on "Evaluating Methods for the Analysis of Rare Variants in Sequence Data" last summer.  

They were recently informed that their project was one of three finalists in the Third Biennial Undergraduate Statistics Project Competition.  They will present their project at next months United States Conference on Teaching Statistics in North Carolina.  During the conference the winner of the competition will be announced.

This is a very competitive competition and congratulations go out to the students and their mentors.

 

Math in the News:  Students attempt to break paper folding record

 
For years, it was thought that a piece of paper could not be folded in half more than eight times.  This was proved that wrong in 2002, utilizing a mathematical formula to demonstrate that the limit was twelve and then succeeding in a 12-fold exercise. Mathematics teacher James Tanton from St. Mark’s School in Southbourgh, Massachusetts has led various groups of students over the past five years in trying to break that mark. They had equaled it twice.

On Sunday, April 3 they again attempted to break the world record for folding paper using two miles of toilet paper.  Using MIT’s 825-foot-long “infinite corridor”, they managed to fold the paper 13 times, using their own mathematical formula. The process took four hours, and the group from Southborough was ecstatic. “It’s like Mt. Everest,” commented Tanton. “Of course we have to try.”

For more information see the Boston Globe article or watch the YouTube video.


Problem Solvers of the Fortnight


In our last our last PotF:  Allyson, Bethany and Corey have a window washing business and are regularly hired by a strip mall owner.  They have found that together they can finish the job in 6 hours less time than when Allyson works alone, 1 hour less than when Bethany works alone, and in ½ the time than when Corey works alone.  The next time they need to wash the windows, only Allyson and Bethany will be able to work.  How long will it take them?
The following students gave correct solutions of an hour and 20 minutes: Eric Lunderberg, Daniel Langholz, Charlie Rowerdink, Tanner Gallant, Ryan Martinez, Tim Nagi, Jeff Shade, Liz Nelis, Sam Pederson, Erica Budge, Katherine Brune, Josh Borycz, Brigid Toner, Eric Hallquist, Kyle McLellan, Kyle Sutton, Matt Eiles, and Matt Rybar.

To see a complete solution to this problem, see Sam Pederson's solution that is posted on the bulletin board outside the Mathematics Department.


Problem of the Fortnight

 
At the last Pi Mu Epsilon induction ceremony, the Math Department served several pies cut into eighths.  Professor Pennings notably favored of the snicker’s pie.  Trying to wait politely for all to be served before taking seconds for himself, anxiety overtook him when he noticed that there was only one slice left and an unsuspecting student was moving toward it.  Professor Pennings swooped in and magnanimously offered to share the coveted delicacy. 

He told the student to cut the piece in half, but not into two congruent wedge shapes, oh no… he told the student to make a cut perpendicular to the cut that most people would make (see picture on the left).  How far from the vertex should the cut have been made so that the two resulting pieces would have the same area?  Give your answer as the ratio between this distance and the radius of the pie, using only a reasonable number of significant digits.

Write a complete solution (not just the answer) and drop it off along with a piece of pie in the Official Problem of the Fortnight Slot outside VWF 212 by 3:00 pm on Wednesday, April 27.  As always, be sure to include your name, the name(s) of your professor(s), and your math class(es) -- e.g. Piper Pike , Dr. Pythagoras, Math 314 -- on your solution. 


   have made this letter longer than usual, because I lack the time to make it short.

Blaise Pascal

Off on a Tangent