Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  October 19, 2011 Vol. 10, No. 3

This week's colloquium takes a look at an old "proof" for the four color theorem

Title: Alfred Kempe's "Proof" of the Four Color Theorem
Speakers: Tim Sipka, Alma College
Time:  Thursday, October 20 at 11:00 am
Place:  VWF 102

Abstract: The four color theorem is a simple and believable statement: at most four colors are needed to color any map drawn in the plane or on a sphere so that no two regions sharing a boundary receive the same color.  It might be surprising to find out that mathematicians searched for a proof of this statement for over a century until finally finding one in 1976.  In this talk we'll consider the "proof" given by Alfred Kempe that was published in 1879 and thought to be correct  until a flaw was found in 1890.  You'll be invited to look carefully at Kempe's proof and see if you can do what many 19th century mathematicians could not do---find the flaw.

Note: We have a nontypical day, time, and location for this week's colloquium.

Next week's colloquium

Title: Lights Out: Some Puzzles, Some Results, and Some Questions
Speakers: Darin Stephenson, Hope College
Time:  Tuesday, October 25 at 4:00 pm
Place:  VWF 104

Abstract:  In the “Lights Out” puzzle, the solver seeks to turn off all of a set of lights (often represented by the vertices on a graph) by pressing a series of buttons, each of which has a certain predefined effect on the lights.  The lights each have an “initial state” (typically “on” or “off”), and an initial configuration of states is called solvable if there is a process for turning off all of the lights.  The solution to any specific version of this puzzle can be phrased in terms of matrix algebra.  Our overall goal is to study this problem in generality, and, eventually, to characterize the solvable initial configurations for certain families of graphs.  In this talk, we will provide a survey of the classical Lights Out puzzle, discuss many generalizations and some known results, and give a few questions that may serve as motivation for collaborative faculty-student research in summer 2012.

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

Help out MDY's Mathemagicians in the upcoming Relay for Life


In the wake of Mary DeYoung’s death after a brief battle with cancer this past summer, many students are looking for ways to honor and celebrate her life. One of these opportunities presents itself in this year’s Relay for Life at Hope College. A team has been formed for all of us to remember Mary DeYoung and to help raise money to fight this horrible disease. You can support the team in any of the following four ways:
  1. Join the team, raise funds, and walk with us at Relay for Life on November 11-12 from 7pm to 7am. If you want to join just go to, click SIGN UP, and then JOIN A TEAM. Look for MDY's Mathemagicians.
  2. Make a donation to team. Either online or by getting the money to one of the team captains: Rachel Elzinga, Morgan Bell, and Nicholle Taurins. There will also be a collection can in the math department office.
  3. Decorate a luminaria in honor of Mary DeYoung or anyone else you know who has been touched by cancer. Luminarias are bags lit by electric lights to honor survivors and people who have lost their battle with cancer. They will line the track during the Relay event and will be honored during a ceremony. Usually people donate $5-$10 for a luminary, but anyone who is interested can make one regardless of whether or not they donate. Simply contact Rachel, Morgan, or Nicholle and we will get you a bag.
  4. Pray for the team as we work to raise money for the American Cancer Society to honor Mary DeYoung.
Even if you can’t join, check out the team page by going to, look for “Top Teams” on the right hand side, click “View All”, and then click “MDY’s Mathemagicians” to see updates on fundraising and team activities.  If you have any questions or ideas please contact Rachel Elzinga (, Morgan Bell ( or Nicholle Taurins (

Thanks for helping us work towards a world with less cancer and more birthdays! 

MATH Challenge

The 2011 Michigan Autumn Take Home Challenge (or MATH Challenge) will take place on the morning (9:30am - 12:30pm) of Saturday, November 5 this year.  Teams of two or three students take a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  Each team takes the exam at their home campus under the supervision of a faculty advisor. 

The department pays the registration fee for each team and will provide lunch to participants afterwards. The sign-up deadline is Monday, October 24 at 4:00 p.m.  Interested students can sign up by sending Prof. Yurk an email at or by signing up on the list on his door (VWF 214).

A group of students may sign up as a team.  Individual students are also encourage to sign up; they will be assigned to a team.  For more information, please talk with any member of the Mathematics Department or visit this link
where you can also view old copies of the exam. 

Math in the News: Scientists use Twitter to analyze public heath trends

Who would ever think that "omg i think i have the flu going home bfn" would be of value to science.  Well according to a recent report from Discoveries and Breakthroughs Inside Science, computer scientists at John Hopkins University are using the online social networking and microblogging service to track public health trends.

"There’s a lot of different patterns we were able to uncover,” said Mark Dredze (Johns Hopkins), “so for example we were able to track the influenza rate in the United States over time just by counting how many times people are talking about the flu.”

Problem Solvers of the Fortnight

In our last problem of the fortnight we saw that Sally began to solve a problem at the time between 4:00 and 5:00 p.m. when the clock's hands are together.  She finished when the minute hand is opposite the hour hand.  How many minutes does it take her to solve the problem, and when does she finish it?  Give exact answers in terms of fractions of minutes (i.e. no decimal approximations).

Congratulations to Lauren Aprill, Ryan Martinez, Lute Olsen, Jessica Hulteen, Jake Blysma, Craig Toren, Krisen Slotman, Corinna Schmidt, Danielle Maly, Erice Budge, Emily Scott, Allison Leigon, Anna Filcik, Lisa McLellan, Kristen Bosch, Bryce Ciroshek, Pete Stuckey, Hunter Ford, Brant Bechtel, Sarah Prill, David Dolphin, Andrew Borror, Morgan Smith, Daniel Langholz, Shinnosuke Kondo, Scott DeClaire, Melanie Leonard, Justin Kammeraad, Allie Benson, Josh Swelt, Kevin Olson, Andrew Brooks, Nicole Zeinstra, Tim Lewis, Tim Cooke, Matt Folkert -- all of whom correctly determined the exact starting and ending time of the exam in the last Problem of the Fortnight.

Problem of the Fortnight

You have ten stacks of coins, each consisting of 10 new dollar coins.  One entire stack of coins is counterfeit, but you do not know which one.  However, you do know the weight of a genuine dollar coin, and you are also told that each counterfeit coin weighs one gram more than it should.  Your kind chemistry professor agrees to let you weigh the coins on one of the electronic scale in the chem lab.

What is the smallest number of weighings necessary to determine which stack is counterfeit, and how do you do it?

Attach a counterfeit dollar coin to your solution, and drop it in the Problem of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00 p.m. on Friday, October  28.  As always, be sure to include your name as well as the name(s) of your professor(s) -- e.g. Bo Guscoins, Professor Cown TerFit -- on your solution. 

The best and most beautiful things in the world cannot be seen or even touched – they must be felt with the heart.

Helen Keller

Off on a Tangent