Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 February 5, 2016 Vol. 14, No. 9

Next week's colloquium: What happens if rooks fly?

Title: What happens if the rooks fly? A combinatorial adventure in three and higher dimensions
Speaker: Feryal Alayont, Grand Valley State University
Time:  Tuesday, February 9 at 4:00-4:50 pm
Place:  VanderWerf 102

In combinatorics, the theory of rooks deals with placements of non-attacking rooks on generalized chess boards and counting such placements. Even though the theory was named after the chess piece rook attacking along rows and columns, the theory was in fact developed to count permutations with restrictions. In this talk, we will investigate the rook theory in three and higher dimensions, inspired by the question “What happens if the rooks fly?” We will show that this theory leads to two different generalizations of the rook placement modeling of the Stirling numbers of the second kind on the triangular boards, starting with two answers to the question “What is a triangular board in three dimensions?” The two answers are intricately related leading to nice results about generalized central factorial and generalized Genocchi numbers. The talk will assume no background in chess or rook theory, and will be a pictorial adventure in combinatorics.

Upcoming Colloquia

The following colloquia are currently on the schedule for this semester. Others will be added as the semester goes along.

  • Tuesday, February 23 at 4-5pm, Stephanie Edwards, Hope College
  • Tuesday, April 19 at 4-5pm, Eric Nordmoe, Kalamazoo College

Stats Showcase

On Friday, January 22, 2016, the Mathematics Department had their annual Statistics Showcase that highlights presentations from their Fall Math 210 Introduction to Statistics classes. This year the following students presented – Allison Hedrick, Logan Meeker, and Quincie Mitchell who were in Jill VanderStoep’s class; Cooper Jennings, Michael Peuler, and Matthew Rose who were in Dawn Verbrugge’s class; Aimée Ndong who was in Yew-Meng Koh’s class, Elizabeth Evenhouse, Courtney Kuemin, and Kaitlyn Tobin who were in Vicki-Lynn Holmes’ class; and Alyssa Pinkham, Michael Shelton and Isabel Wanyagah who were in Todd Swanson’s class.

Math Club News

The Math Club invites you and your friends to The Theory of Everything on Friday, February 5 at 9:00 pm in Winants Auditorium in Graves Hall.  The movie features the life of Stephen Hawking, one of the world's foremost physicists.  The movie tells the heartfelt story of Stephen falling in love with arts student Jane Wilde and raising a family, all while his body is failing him and his popularity soars as his brilliant ideas become widely known.

For more info on the Hope Math Club's latest and greatest activities, visit their FaceBook page (and request to join the group).

Math Summer Research

It's 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:  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. 

There are also opportunities available for summer research in mathematics at other institutions.  You can find a list of NSF funded Research Experience for Undergraduates in mathematics here


Math in the News: Did Ancient Babylonians know Calculus?

It has been known that ancient Babylonians tracked the orbits of the moon and other objects in the sky by using a series of  additions, subtractions, and multiplications----all in base-60. It has also been known that they used some basic geometric concepts to help with calculations on earth.

Recently, however, a tablet in the British Museum has been deciphered and appears to show that they used geometry to track Jupiter. A trapezoid was used to calculate the first 120 days of Jupiter's orbit. To calculate when Jupiter reaches the midpoint in the first half of this orbit involved taking the left half of a trapezoid and dividing it into two parts that have equal area. The approach the Babylonians used to figure this out is similar to integration in calculus. While they probably didn't go this far since they only divided the trapezoid a few times, it does show that they recognized the general approach integration.

For more information about this visit an article in Ars Technica

Math Road Trip

On Saturday, February 27 the Math in Action Conference at Grand Valley State University presents lively and informative discussions of current issues in mathematics education while providing an opportunity for practicing PreK – 12 teachers, prospective teachers, curriculum directors, and college and university faculty to share ideas, concerns, and resources. The conference consists of six hour-long sessions with eight separate interactive presentations during each and is an opportunity for Hope Mathematics and Mathematics Education majors to attend great conference close to home.

For Hope College Mathematics and Math Education Majors, student registration fees and transportation via a Hope College Van will be covered by the Math Department and is being organized by Dr. Mann.  Drop him an email at or stop by his office, VanderWerf 213, to find out more or reserve your seat in the van by Thursday, February 11.

Problem Solvers of the Fortnight

In our last POTF we showed a square of side length 2 and a circle that shared the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?

Congratulations to Robert Abbaduska, Shawn Bates , George Becker Rust, Luke Boggs, Brandon Bowser, Owen Brooks, Josiah Brouwer, Landon Brower, Aaron Cendejas, Josh DeRitter, Alex Dolehanty, Alexander Donán, Brooke Draggoo, Grace DuMez, Conner Gentry, Zach Geschwendt, Jason Gomory, Alek Gohrmann, Mariah Heady, Katlyn Hettinger, Emily Hormeyer, Russell Houpt, Jesse Ickes, David Inman, Eddie Ip, Young Jin, Eric Johnson, Tom Johnson, Michael Kiley, Jacob Knol, Noah Kochanski, Elizabeth Koning, Jessica Korte, David Lunderberg, Chris McAuley, Taylor Myer, Joshua Nkonge, Monica Ohnsorg, Jackie Plowman, Cam Pratt, Miles Pruitt, Andrew Ragains, David Rak, Jessica Reichenbach, Jada Royer, Natalie Schalk, Jacquelyn Schwark, Andrew Shay, Emma Smalley, Daria Solomon, Regina Tan, Tristan Tobias, Kathryn Trentadue, Shannon Urbanik, Nathan Vance, and Jim Williamson -- all of whom correctly solved the Problem of the Fornight in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

Are there any positive integers x, y, and z that simultaneously satisfy the following equations?

3x2 = 2y2 + 4z2 - 54 and 5x2 = 3y2 + 7z2 - 74

If so, find them.  If not, show why not.

Attach your solution to a ski lift ticket (preferrably one that's valid for a local ski hill on one of the days of Winter Break) and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Friday, February 12.  As always, be sure to include your name as well as the name(s) of your math professor(s) -- e.g.  Ben Thinken, Professor Stu Pendus-- on your solution. 

Pure mathematics is the world's best game.  It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly.  It's free.  It can be played anywhere - Archimedes did it in a bathtub. 

~Richard J. Trudeau, Dots and Lines

Off on a Tangent