Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  January 17, 2011 Vol. 9, No. 8 
http://www.math.hope.edu/newsletter.html


The first colloquium will focus on geometry


Title:  The Teetotaler's Tour: A Simple Strategy for the Aspiring Globetrotter
Speaker: Dan Visscher: Graduate Student, Northwestern University
Time:  Tuesday, January 18 at 4:00 p.m.
Place:  VWF 104

Abstract: Is it ever effective for the aspiring globetrotter to simply walk straight, never changing directions during her travels?  We will investigate this method of exploring a surface, considering a couple of different geometries and the effects they have on the above question.  Only a subset of geometries can occur on a sphere and we will discuss what can happen when our straight-walking globetrotter finds herself on the earth.

 

Colloquium Schedule

Below is the tentative colloquium schedule for this semester.

  1. Tuesday, January 18, 4PM—Dan Visscher, Northwestern University
  2. Tuesday, February 1, 4PM—Randall Pruim, Calvin College  (postponed until  Thursday, February 17 at 4PM)
  3. Thursday March 3, 4PM—David Murphy, Hillsdale College,
  4. Tuesday March 15, 4PM—John Gabrosek, Grand Valley State University
  5. Friday April 1, 3PM—Clay Cressler, University of Michigan
  6. Tuesday April 12, 4PM—Darren Parker, Grand Valley State University
  7. Tuesday, April 19, 11AM—Matt Boelkins, Grand Valley State University
  8. Tuesday, April 26, 4PM—Melinda Koelling, Western Michigan University

 

Summer Research

It is time to start thinking about summer!  The mathematics department will host a number of research students this summer.  Typically projects run for eight weeks and students earn a stipend for their participation.  Projects include work in the mathematical biology, statistics, mathematical modeling, graph theory, and mathematics education.

Descriptions of research projects can be currently found at the online application site: http://sharp.hope.edu/.  If you are interested in applying for summer research at Hope, please talk to any of the math professors.  Applications are due by February 15. 



Math in the News:  The Mathematics of a Snowflake

Mathematicians have developed a computer program that models the growth principles of snow crystals. Using mathematical equations repeated billions of times, the program creates snowflakes that look like they tumbled right out of the clouds.  In real clouds, snow crystals form in the shape of hexagonal prisms. As they grow, branches sprout from the corners, creating ever more complex shapes. Conditions such as temperature and humidity in the atmosphere also influence their shapes.

For more information and to view a video of a computer snowflake being formed, go to the article from Discoveries and Breakthroughs inside Science found here.


Problem Solvers of the Fortnight


We had the following problem in our last newsletter: Suppose a cubic polynomial with leading coefficient of one and with inflection point at the origin passes through (c,0) and (a,b), where a>c>0.  A translated copy of the cubic has its inflection point at (a,b) and passes through the origin.  Show that twice the area between the two cubic polynomial curves equals a4.

The following students gave correct solutions: Emily Rowland, Tanner Gallant, Elizabeth Mosley, Bobby Cawood, Teagan Quinnell, Katie VanDenburgh, Joshua Kammeraad, Tom Smeltzer, Morgan Smith, Josh Franz, Kim Slotman, Dan Irvin, Ben Thomas, Eric Greve, Alayna Ruberg, Curtis Drozd, Adam Clements, Jakob Gibson, Elizabeth Veenhoven, Brandon Jonker, Lydia Benish, Joel Brogan, Nathan Dwight, David Gansen, Craig Toren, Cortney Kimmel, Rob Peterson, Morgan Bell, Joshua Borycz, Justin Hanselman, Steve Higgins, James Bow, Phillip Hllam, John Bain, Emily Nock, Scott DeClaire, Eric Lunderberg, and Ryan Martinez.


Problem of the Fortnight


Over the break I decided to finally organize some of the books on my office shelves.  In particular, there was a stack of six books on the edge of one shelf that were threatening to topple onto my monitor.  From the clues give, determine the titles, authors, color of the spine, and position in the stack (top of stack is book #1). 

Clues:
  1. The textbook Calculus is immediately below the book by Bernard but somewhat higher in the pile than the book with the bronze colored spine.
  2. Hogg and Tanis' text, Probability and Statistical Inference, is two books below the royal blue book.
  3. The bottom book in the pile (position #6), which was not written by Edwards & Penney, is an aqua color.
  4. The white book is by Thompson, and it occupies an even-numbered position in the pile.
  5. The navy colored book has a somewhat vague title: Mathematics.  Its position number is not a perfect square.
  6. An old all-time favorite read, Calculus Made Easy, occupies position #4 in the stack.
  7. The book with the tan spine is not Differential Equations.
  8. The author of the book at the very top of the stack is Peterson.
  9. Former Hope professor, J. Van Iwaarden, is the author of one of the books.
  10. The book titled Algebra is higher in the stack than Calculus.

Write a complete solution in your favorite math book and drop it off in the Official Problem of the Fortnight Slot outside VWF 212 by 3:00 pm on Wednesday, January 26.  As always, be sure to include your name, the name(s) of your professor(s), and your math class(es) -- e.g. A. D. Powers, Dr. Evil, Math 123 -- on your solution. 


Most great people have attained their greatest success just one step beyond their greatest failure.

Napoleon Hill


Off on a Tangent