Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 March 4, 2016 Vol. 14, No. 11

Next week's colloquium: Math and Art

Title: The Creative World Where Math and Art Collides
Speaker: Paul Yu, Grand Valley State University
Time:  Tuesday, March 8 at 4:00-4:50 pm
Place:  VanderWerf 102

In a world where many dichotomize Mathematics and Art as left and right brained activities, Dr. Yu shares his experiences as a mathematician, artist and educator in which these seemingly divergent disciplines intertwine.  The common strand connecting these disciplines is the role of aesthetics, a response in which a mathematician can see a proof as elegant, an artist can see a painting as beautiful, and an educator see a lesson as artful.   While the criteria for the aesthetic qualities of these disciplines may differ, they all share the common element of a meaningful emotive response.

Upcoming Colloquia

There is one more colloquium that is currently on the schedule for this semester.
  • Tuesday, April 19, Eric Nordmoe, Kalamazoo College

Lower Michigan Mathematics Competition

The 40th Annual Lower Michigan Mathematics Competition (LMMC) will be held at Hope College this year on Saturday, April 9.  Students from colleges and universities in Michigan will gather to challenge themselves on ten interesting problems, working together in teams of up to three people. The competition takes place in the morning and after lunch there is a discussion of the solutions. 

If you want to participate, you must sign up by Tuesday, March 29 (the day after spring break) by sending Prof. Cinzori's an email at  You may register as a team (of two or three) or individually (and you will be placed on a team).

The picture shown with Hope Students holding the Klein Bottle Trophy for winning the LMMC is getting a bit old. It would be nice to have a victorious team so this picture could be updated!

Summer workshop on big data available to undergraduates

The University of Michigan Biostatistics Department, in cooperation with the Electrical Engineering & Computer Science and Statistics departments, is running a six-week workshop this June and July in Ann Arbor on big data, targeted specifically at undergraduates. There is no cost to attend, and accepted applicants will receive a stipend to cover living expenses.

Lectures will be led by a diverse group of stellar biostatistics, statistics, electrical engineering, and computer science faculty at the University of Michigan. Working in teams, students will participate in mentored big data research projects.

Application closes March 15, 2016. For more information about the workshop and an application visit

Department hosted Pizza and Game Night

"Let it never be said that the math folks don't know how to have fun!" quipped Dr. Andy McCoy, director of the Ministry Studies program at Hope, as he passed by the room where raucous laughter was erupting from the math department's Pizza and Games night this past Wednesday night.  Hope students, as well as math professors and some of the professors' kids, all enjoyed an evening of food and fun together.  Thanks to Drs. Yurk and Koh for their work in organizing this event, and thanks to all the students who helped make it such a fun evening.  

Students travel to Mathematics Education Conference

On February 27th, five mathematics education students attended the Math in Action conference at GVSU with Dr. Mann.  Sessions covered a variety of topics including the use of online resources such as and, the challenge of promoting perseverance in the classroom, math magic tricks, and number talks.

Upon their return, the Hope students were excited to have been exposed to a plethora of resources that could be used in their future classrooms. The Math in Action conference was valuable opportunity to dialogue with other preservice teachers and with educators coming from a variety of backgrounds.  Other math educators would benefit greatly from attending this conference in the future.

Math in the News: Zipf's Law and Project Gutenberg

Zipf's law, named after linguist George Zipf, states that the frequency of any word is inversely proportional to its rank. Thus the most frequently occurring word will appear approximately twice as often as the second most frequently occurring word, three times as often as the third most frequently occurring word, and so on.  This same relationship is supposed to hold true with other rankings such as population ranks of cities, income rankings, and so on.

Zipf's law was recently tested using the entire collection of English-language texts in the Project Gutenberg, a freely accessible database with over 30,000 books in English. According to a report in, in an analysis where the rarest words are left out (those that appear only once or twice throughout a book) 55% of the texts fit Zipf's law and if all the words are taken into account then 40% fit Zipf's law.

How might this edition of Off on a Tangent fit Zipf's law?

Problem Solvers of the Fortnight

In our last POTF we showed a vertical circular disk of radius R that was partially submerged in a liquid.  The disk rotates, so that the portion that was submerged becomes exposed to the air, allowing the liquid to evaporate.  Assuming that the disk is spinning fast enough so that the liquid stays within the annulus shown in the figure, at what height above the surface of the liquid should the center of the disk be placed in order to maximize the area of the exposed portion of the annulus and thereby maximize the efficiency of the evaporator?

Congratulations to Zach Geschwendt, Jesse Ickes, and David Rak, who correctly solved the Problem of the Fortnight in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

Suppose three red checkers and two black checkers are arranged in an alternating pattern along a line (as shown in the figure below).

You are allowed to move the checkers as follows: By placing the tips of the first and second fingers on any two touching checkers, one of which must be red and the other black, you may slide the pair to another spot along the line.  The two checkers in the pair must touch each other at all times.  The checker at left in the pair must remain at left; the checker at right must remain at right.  Gaps in the chain are allowed at the end of any move except the final one.  After the last move the checkers need not be at the same spot on the line that they occupied at the start. 

A.  What is the smallest number of moves that will rearrange the checkers so that the three red checkers are on the left and the two black checkers are on the right (as shown in the figure below) -- and how do you do it? 

B.  Now answer the previous question assuming now that you are allowed to move two checkers of the same kind.

Write your solution on a single sheet of paper, with part A on one side and part B on the other.  On your solution, show the configuration of numbered checkers that results from each move (along with a short description of what each move does), and at the end, clearly indicate the total number of moves. 

Drop your solution in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 on Friday, March 11.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Bobbi Fisher, Professor Casper Rove -- on your solution.  Good luck, and have fun!

Mathematics is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry.
Oswald Veblen

Off on a Tangent