Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
March 3, 2017 Vol. 15, No. 10

The first Pi Day colloquium will take a look at paradoxes

Title: Mind-Bending Paradoxes & the Possibility of Changing Your Mind
Speaker: Dave Kung, Ph.D, Department of Mathematics, St. Mary's College of Maryland
Time: 11:00 a.m. on Tuesday, March 14, 2017
Place:  VanderWerf 102

Great riddles and paradoxes have a long and illustrious history, serving as both tests and games for intellectual thinkers across the globe. Passed through the halls of academia and examined in-depth by scholars, students, and amateurs alike, these mind-benders have brought frustration and joy to those seeking intellectual challenges. Choosing to confront these conundrums, we put ourselves in that special moment when we acknowledge that what we previous thought conflicts with some new piece of evidence. Those are the moments - rare and precious - when we might actually change our minds! Topics will range from the philosophical to the statistical, from physics to psychology, all from the perspective of a mathematician. Prepare to have your mind bent - and maybe even changed.

The second Pi Day colloquium will explore the connection between mathematics and music

Title: Theory & Practice: Mathematics and Music
Speaker: Dave Kung, Ph.D, Department of Mathematics, St. Mary's College of Maryland
Time: 4:00 p.m. on Tuesday, March 14, 2017
Place:  VanderWerf 102

The two subjects of math and music are connected in myriad ways, from the rhythm of notes to the frequencies of the pitches. At the advanced level, both mathematical theories and music theories help us understand the other subject. In this talk, we first explore what mathematics tells us about musical instruments, the basic tools of musical practice. In the second half, we flip sides, looking at music theory and how the structure of chords gives us another way to understand topological structures (circles, Möbius strips and higher dimensional tori), some of the basic tools of mathematical practice. Thus the first half connects mathematical theory to musical practice, and the second connects musical theory to mathematical practice. Throughout, examples played on the violin will illustrate all of these beautiful and surprising connections.

Upcoming Colloquia

We have the following additional math colloquia on the schedule for this semester. More will most likely be added.
  • Thur, Apr, 20 at 4:00 PM in VWF 102: Dr. Lauren Keough - GVSU
  • TBA, Dr Tim Pennings - Davenport University

 Math Spring 2017 Game and Pizza Night

Come eat pizza and play games with your fellow math students and the math department on Monday, March 6! 

We will meet in VZN 247 starting at 6PM for an evening of fun, adventure, and intrigue. Sign up in your math class or outside of VWF 210 (Dr. Koh’s office). It will be more fun than a barrel of monkeys!

Textbook receives national award

Introduction to Statistical Investigations is receiving a 2017 Most Promising New Textbook Award from the Textbook and Academic Authors Association. The awards recognize excellence in first-edition textbooks and learning materials based on pedagogy, content and scholarship, writing, and appearance and design.

The initial version of the text was written and piloted by former Hope faculty Nathan Tintle and current Hope faculty Todd Swanson and Jill VanderStoep in 2009. Since then, four more authors were added to the team and after many revisions, the text was published by John Wiley & Sons in 2015.


Ever wonder what a math major and art minor might be thinking about or how she views the mathematics that you are seeing in your classes? Check out Caroline's blog called eigenstuff. She has some pretty cool pictures of her creations where you can see how mathematics looks to her.

Lower Michigan Mathematics Competition

The 41st Annual Lower Michigan Mathematics Competition (LMMC) will be held at UM-Flint this year on Saturday, April 8.  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 Wednesday, March 15 (right before 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!

Problem Solvers of the Fortnight

In our last problem of the fortnight we saw that the saga between Math Man and Vectoria continued as follows:

"Hey, M's.  How's it going?"
"Oh, not too bad, thanks.  How are you?"
"Great!  I just got back from a camping trip.  It was awesome!"
"You took a camping trip over Winter Break!  Are you nuts?"
"No, we went camping down south.  It wasn't too cold.  And it didn't even rain!  What did you do over break?"
"Not much, really.  Although I did find a neat problem.  I haven't been able to solve it, but it seems like it's neat."
"What is it?"
"Take a triangle -- let's say its sides are 3, 5,  and 7, although I think they could be anything."
"Well, not anything, they'd have to satisfy the triangle inequality."
"Well, okay, fine.  What I meant was that there's nothing special about the sides being 3, 5, and 7 in particular.  They just happen to be for this particular triangle."
"Okay, I'm with you.  We've got a 3-5-7 triangle.  What's next?"
"Call the vertices A, B and C, and draw line segments from each vertex to the midpoint of the opposite side.  Designate as a the length of the segment originating at vertex A, b the length of the segment originating at B, and c the length of the segment from vertex C."
"Got it.  So it looks something like this," says Vectoria, showing Math Man the sketch she drew.

"Yeah, wow!  How did you know those line segments all meet in a single point?  That took me three days to try to prove."
"Oh, that's a result from geometry.  I think we learned it in high school.  I don't remember how to prove it, but I do remember that result because it seems like a tremendous coincidence that those three lines would all cross in a single point.  Almost magical."
"Right.  Well, it is a tremendous coincidence.  Or maybe a tri-mendous coincidence!"
"Never mind."
"Whatever. . . .  So?"
"So what?"
"So what's the problem, Double M?!?!"
"Oh, right.  It's easy.  To state, I mean.  I don't know whether it's easy to figure out.  I mean, I haven't yet. . . ."
"Right.  Sorry.  The problem is to figure out a2 + b2 + c2."

Congratulations to Richard Edwards, Christian Erickson, Jason Gombas, Erik Johnson, Karthik Karyamapudi, Jenna King, Philip LaPorte, Nick Lillrose, Dane Linsky, David Niewoonder, Alex Osterbaan, Zheng Qu, Hugh Thiel, Neil Weeda, and Jincheng Yang -- all of whom correctly solved the Problems of the Fortnight in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight

"Hi Vectoria."
"Hey M's.  What's up?"
"Well, I have a question for you.  Your birthday's coming up, isn't it?"
"Yeah, it sure is!"
"Okay, then I have another question for you."
"Oh, c'mon, Double M!  You know when my birthday is!"
"No, yeah, I do.  I wasn't going to ask you that."
"Oh, my bad.  Go on."
"I was going to get you a chocolate bar from The Peanut Store."
"Oh, M's that's sweet.  But usually people keep birthday gifts a secret."
"Yeah, I know."
"Then why are you telling me what you're getting me?"
"Well, the chocolate bar isn't the gift, really.  The gift is this problem I got to thinking about.  I mean, I know you really like math problems, and I figured none of your other friends would give you a problem for your birthday."
"Awww, M's.  That really is sweet.  Thank you.  So what's the problem?"
"Okay.  So the other day at the Peanut Store, the owner -- who's a really nice guy, I have to say -- showed me a special chocolate bar he had in the back room after I told him I wanted to get something special for my friend's birthday.  The chocolate bar had two rows with 10 dark chocolate squares in the top row and 10 white chocolate squares in the bottom row."
"Sort of like a black and white cookie -- but a chocolate bar instead."
"Exactly. Now, I know you have a number of good friends, and you'd probably want to share with them, right?"
"Yeah, probably."
"So, not knowing what kinds of chocolate your friends like, I got to thinking about the different ways you could break it up.  And when I was thinking about it, I realized you'd probably enjoy the problem as much as the chocolate bar.  So here you go.  Suppose you break it entirely into pieces of size 2 x 1 (which have one brown square and one white square), pieces of size 1 x 2 (which have either two brown squares or two white squares, depending on which row they came from) and pieces of size 2 x 2 (which, of course, have two brown squares and two white ones).  In how many different ways can you break the chocolate bar into pieces of size 1 x 2, 2 x 1 and 2 x 2?"
"Hmmm. . . .  That is a fun problem. . . .  Let me play around with it, okay?"
"Sure.  See if you can figure it out before I give you the chocolate bar on your birthday."
"Cool!  Thanks, Double M!"

Help Vectoria determine how many different ways she could break the chocolate bar into 1 x 2, 2 x 1 and 2 x 2 pieces.  Write your solution on either the back of a candy bar wrapper or on a piece of paper that is affixed to a chocolate bar, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (Vander Werf 212) by 3:00 p.m. on Friday, March 10.  As always, be sure to include your name, as well as the name(s) of your math professor(s) -- e.g. Manny I. Diaz, Professors Ben Thinkin and Ivan Ocean -- on your solution.  Good luck and have fun!

Sinusoidal Snow Graffiti

Off on a Tangent