Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  November 16, 2011 Vol. 10, No. 5
http://www.math.hope.edu/newsletter.html


This week's colloquium will answer the question, "Do dog's know calculus?"

Title: Do Dog's Know Calculus
Speakers: Tim Pennings, Hope College
Time:  Thursday, November 17 at 4:00 p.m.
Place:  VWF 104

Abstract: A standard calculus problem is to find the quickest path from a point on shore to a point in the lake, given that running speed is greater than swimming
speed. Elvis, my Welsh Corgi, has never had a calculus course. But when we play "fetch" at Lake Michigan, he appears to choose paths close to the calculus answer. In this talk we reveal what was found when we experimentally tested this ability. Elvis will be available for follow-up questions.

Note: Please come to enjoy  refreshments with the speakers, the faculty, and fellow mathematics students before the colloquium at 3:30 pm in VanderWerf 222.


How to win the game Lights Out!

Title: The Generalized Lights Out Game on Graphs
Speakers: Darren Parker, Grand Valley State University
Time:  Tuesday, November 22 at 4:00 p.m.
Place:  VWF 104

Abstract: The game Lights Out is an electronic game by Tiger Electronics.  One begins with a 5 by 5 grid of lighted buttons. Some of the lights are on and some are off.  Each time a button is pressed, the button pressed and the adjacent buttons change from on to off or vice versa.  The game is won when all the lights are turned out.
Lights Out can be generalized so as to be played on graphs, where the edges of the graph define what it means for two of the lights to be adjacent.  Otherwise, the game is played as before.  We can generalize the game further by allowing more than one "on'' state (think of it as different colors that the lights can have).  In this case, lights do
not simply switch between "off'' and "on'' when buttons are pressed.  They cycle through all possible colors.  In this talk, we will work our way toward understanding the
generalized Lights Out game.  In particular, we seek to develop strategies to win the game when the graph is a path graph or a cycle graph.  We determine for which of these graphs the game can be won regardless of the initial states of the lights.

Note: Please come to enjoy  refreshments with the speakers, the faculty, and fellow mathematics students before the colloquium at 3:30 pm in VanderWerf 222.

Hope students participate in MATH Challenge

 
Hope students worked in teams of three to complete a difficult three hour mathematics examination as part of the 17th annual Michigan Autumn Take Home (MATH) Challenge. They competed with students from 24 different colleges and universities from across Michigan and the rest of the United States. With 12 teams, Hope had the largest number of students in the competition (other institutions had at most six teams).

The students that participated in the exam were:  Matt Eiles, Caitlin Taylor, Kiley Spirito, Nathan Graber, Jess Bolkema, Eric Grieve, Bobby Nash, John Bain, Tristan Zintl, Byonjoo Bark, Dominic Surya, Sydney Bryer, Brooke Jeries, Holly Drummond, Josh Kammeraad, David Dolfin, Matt Johnson, Nick DeJongh, Taylor Brushwyler, Craig Toren, David Schroeder, Luke Platte, Drew Cook, Samantha Kemperman, Yijun Liao, Connor Berrodin, Dan Simpson, Eric Lunderberg, Eric Halquist, Nick Boersma, Chris Beaudoin, Brian Bjerke, Justin Knutter, and Hsiang Lin.


Math Club meeting tonight!



The Hope College Math Club meets again!

We will be meeting in VanderWerf 237 at 7:00pm on Wednesday, November 16 to hang out, enjoy snacks, plan events, and brainstorm t-shirt designs. Bring some friends and t-shirt ideas!

Hope to see you there!


Problem Solvers of the Fortnight

     
In the last problem of the fortnight, we saw that four bugs, (A, B, C & D) occupied the corners of a square 10 inches on a side. Simultaneously, A crawls directly toward B, B toward C, C toward D, and D toward A.  If all four bugs crawl at the same constant rate, they will describe four congruent logarithmic spirals that meet at the center of the square.

How far does each bug travel before they meet?  

Congratulations to our Problem Sovers of the Fornight -- Eric O'Brien, Eric Hallquist, Parker Millington, Eric Westenbroek, Tim Cooke, Brian Ward, Seth Blythe, John Lithio, Derek Boat, Andrew Brooks, Evelyn Ritter, Corntey Kimmel, Aaron Mick, Nick Johnson, Ryan Martinez, Patrick Malley, Zac Lockhart, Seth Coffing, Lauren Aprill, Andrew Borrar, Todd Scott-Dettl, Jordan Gowman, Caitlin Kozack, Steph Vincent, Nicholas DeJongh, David McMorris, Sam Pederson, Isabel Morris, Andreana Rosnik, Erin Farrey, Leah LaBarge, Charlotte Korson, Kelsey Cooper, Sarah Prill, Austin Homkes, Andrew Cutshall, Josh Swelt, Tanner Gallant, Joe Wierzbicki, Julia Austin, Tessa Schultz and Kyle Coggins -- all of whom correctly reasoned that the bugs have to travel 10 inches before they meet.


Problem of the Fortnight


When the celebrated German mathematician Karl Gauss (1777-1855) was nine years old, he was asked to add all the integers from 1 through 100. He quickly added 1 and 100, 2 and 99, and so on for 50 pairs of numbers each adding in 101.
His answer was 50 · 101 = 5050.

Now find the sum of all the digits in the integers from 1 through 1,000,000 (i.e. all the digits in those numbers, not the numbers themselves).

Drop off your solution in the Problem of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00 p.m. on Wednesday, November 23.  As always, be sure to include your name as well as the name(s) of your professor(s) -- e.g. Georg Riemann, Professor Karl Gauss -- on your solution.  (Riemann was actually one of Gauss's students)


Talent is cheaper than table salt. What separates the talented individual from the successful one is a lot of hard work.

Stephen King

Off on a Tangent