Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
October 14, 2016 Vol. 15, No. 3

Annual Gentile Lectures will feature a computational mathematics scholar

Title: History of Computing and Its Role in Society
Thursday, October 20 at 7 p.m.
Place: VanderWerf 102
Title: Paradigm Shifts in Parallel Computing for Implicit Methods
Time: Friday, October 21 at 3 p.m.
Place: Winants Auditorium of Graves Hall
Speaker: Dr. Andrew Christlieb, Michigan State University Department of Computational Mathematics, Science and Engineering

Andrew Christlieb, chair of the MSU's Department of Computational Mathematics, Science and Engineering will present two lectures as part of the Gentile Lecture Series. He will present “History of Computing and Its Role in Society” on Thursday, Oct. 20, at 7 p.m. in room 102 of VanderWerf Hall, and “Paradigm Shifts in Parallel Computing for Implicit Methods” on Friday, Oct. 21, at 3 p.m. in Winants Auditorium of Graves Hall. 

Upcoming Colloquia

The  following additional colloquium is on the schedule for this semester, but more should be added.
  • Thursday, November 17, Victor Piercey, Ferris State University

Interview with Aaron Green

Aaron Green is a double major in Mathematics and Computer Science at Hope College and we thought his experiences at Hope would be interesting to share with other current students, especially younger students who are trying to determine their interests and understand the opportunities that exist here at Hope.

Aaron, you're a math and computer science (CS) double major at Hope College.  You've done interdisciplinary math and computer science summer research at Hope and have just finished a summer internship in Madison, Wisconsin.  Could you please tell us more about these experiences, what you enjoyed most, and how these experiences have helped you find your future vocation?
I worked on research relating to Graph Pebbling with Professors Charles Cusack and Airat Bekmetjev from the Computer Science and Math departments, respectively. I worked with one other student, Cole Watson, who is also a math and computer science double major. I greatly enjoyed my research during that summer and have actually continued that research off and on with those same people. Prior to taking part in that summer research, I thought that I wanted to be a software developer in the future. I considered Computer Science to be my primary major and was majoring in Math because I found it somewhat interesting, but I did not expect to enjoy the mathematics of my research as much as I did. I wrote a good amount of code during research and I enjoyed writing that code, but my favorite part of research was really the theoretical side of it. The combination of computer science and mathematics was interesting and very enjoyable to me, and it made me realize that my majoring in math was a very good decision.

Last summer I worked as a Software Developer intern with Epic Systems in Madison, WI. Epic Systems is the nation’s largest health care software provider, covering almost 60% of the U.S. My job at Epic was what I consider to be a very typical software developer position. I was working with code almost all of the time. My project was to design an application that could analyze workflows throughout a hospital of doctor’s office and find places in the workflows that are inefficient. While working on this project, there was not really enough time for me to work on the theory of the problem that was trying to be solved since I only had eleven weeks with Epic. I had to spend the vast majority of my time working with code, which was what I thought that I wanted to do. However, I found that I really missed the theoretical aspect of the work. It was a great experience, but it showed me that I do not want to just be a software developer, but rather would work with the theory of computer science in the future. That is why I have decided to pursue a graduate degree in computer science.
I can see your interests in what you want to study have evolved while at Hope, but could you be more specific and tell us what you like most about mathematics and computer science as well as what opportunities you would encourage other students to take explore?

My favorite part about math and computer science is the theory of it all. There are so many important problems that have yet to be solved and that people have been working on for a long time. It is exciting to imagine working on some of these problems and potentially finding solutions to them, or even just finding clever ways around them. I would encourage anyone who is genuinely interested in math to look into doing summer research with one of the math professors here. It will give you the chance to apply the things you have learned from the math classes you have taken to some real, interesting, and challenging problems. You will likely gain a lot of new respect for math when you get to use it to solve difficult problems in novel ways.

Thanks. Summer research opportunities for next year will become more developed and publicized next semester, but it not too early to talk to mathematics professors about one's interest in doing summer research. As a final question, could you please share with us something interesting about yourself?
One interesting thing about me is that I was asked to be interviewed for the world’s premier fortnightly newsletter, Off on a Tangent. Another interesting thing about me is that I am involved in the Holland chapter of the No Rules Association (if you are curious what this is, email me at
Also there actually are no rules at all in the NRA.

 Students present at mathematics education conference

Professors Jane Finn and Vicki-Lynn Holmes, student teachers (and Hope College students) Jessie Hermann and Grace Wiesner, along with Zeeland East mathematics teacher Kristin Lohr recently presented at the Michigan Council of Teachers of Mathematics conference on making Math Meaningful Through Collaboration.

They talked about the collaboration between Zeeland East Public Schools and both the Special Education and Math departments here at Hope.  Through the collaboration, they developed a workbook for struggling algebra students. To create the workbook, Hope math and special education teacher candidates created math lessons that incorporated different curriculum content areas, taught these lessons to Zeeland at risk students. They were critiqued by the Zeeland master teacher, the students, the professors and the students for both pedagogy and content.

Problem Solvers of the Fortnight

In our last Problem of the Fortnight we presented the following conversation between Math Man and Prof. Vance:

Hi, Professor Vance!
Oh, hi, Math Man.  How are you?
Just fine, thanks.  But I'm a little puzzled at the moment.  I found this diagram on a piece of paper outside your office door.  I think one of your students must have dropped it.
Well, puzzle no longer, Math Man.  I can tell you whose that is!  It's actually mine -- and I need it for my class today.  So, I'm really glad you found it.  Thanks, Math Man!
Well, sure.  Happy to help.  But I wasn't really puzzled about whose paper it was.  I was puzzled about what the diagram is supposed to be showing.
I can help you there, too!  It's a proof of the law of cosines.
Really?!?  That's neat! . . . .  Just one question: what's the law of cosines, and how does this picture prove it?"
I think that was two questions.
Well, I wasn't sure how to count that compound sentence.  I mean, there are two questions, but they're joined by a conjunction to make a single sentence. . . .  Well, whatever.  Can you help me understand this?
Sorry, Math Man, I can't right now.  I have to run to class.  Thanks for finding this diagram, though!
But wait!  Could you just tell me what the law of cosines is?

On her way out the door, Professor Vance says, "Not right now, Math Man.  Sorry.  I'm running late as it is.  You can Google it, though."
"Yeah, I suppose.  That will tell me what the law of cosines is, but how in the world is this diagram supposed to prove anything?"
Walking down the hall, Professor Vance turns and, walking backwards, says, "That's a good puzzle for you.  You figure it out!"

Congratulations to Josiah Brouwer, Brandon Brown, Richard Edwards, Russell Houpt, Lara Iaderosa, Jiyi Jiang, Emily Joosse, Karthik Karyamapudi, Cassidy Kessel, Eric Krzak, Philip  LaPorte, Izzy Mandelbaum, Emily Martin, Benjamin Pederson, Cole Persch, John Peterson, Zheng Qu, Jada Royer, Sarah Seckler, Caren Shin, Nancy Sierra, Daria Solomon, Elizabeth Sumner, Melah Travis, Hannah Weeldreyer and Samartha Yacullo -- all of whom correctly solved the Problem of the Fortnight in the last issue of America's premiere fortnightly electronic mathematics department newsletter.

Problem of the Fortnight


"Hey, Math Man.  What are you looking at?"
"Oh, hi, Vectoria.  I'm trying to figure out this geometry problem."
"Oooh!  What is it?  I love geometry!"
"Well, we have a quadrilateral ABCD, and ABC and ACD are similar right triangles with right angles at B and C respectively."
"Okay, I'm following.  Go on."
"This point E here is the midpoint of BC."
"Yeah, okay. . . ."
"Well, the problem is to show that BD and AE are perpendicular."

"Hmmm . . . .  That is an interesting problem.  Let me think . . . ."
After a while, Vectoria exclaims, "Got it!  Wow, that is a cool problem, M2 -- and you can solve it using vectors!  In case you didn't know this already, I like vectors a lot!"
"I hadn't made that connection before, but now that you mention it, it makes perfect sense. . . . Or wait, I would have thought that your parents were the ones who really like vectors, since they named you Vectoria."
"Well, they do, but I like them a lot too.  Our family was always headed in pretty much the same direction."
"Oh, I see. . . .  But wait, do you need to use vectors to solve this problem?"
"No, I wouldn't think so.  But if you do know a little bit about vectors, the solution's quite elegant."  After a brief pause, Vectoria says, "Well, see you later, Math Man.  I need to head out now."
"Wait, can't you stay to tell me the solution?"
"Nope, sorry, M2.  Gotta run."
"Well, can you stay long enough for me to take a selfie with you?  I mean, everyone's going to want to know what you look like!  And besides, I kinda don't like being the only one in these photos."
"Nope, sorry again, friend.  I really do need to run.  Maybe next time, okay?"
A little dejected, Math Man says, "Okay, yeah, maybe next time. . . .  See ya!"
On her way down the hall, Vectoria turns and says, "Yeah, see ya later, Math Man.  Have fun working on the problem!  It's a good one!"

At that moment, Math Man pulled out his phone to try to get a picture. However, either Vectoria was too fast or Math Man was too slow, so all he got was the picture shown. Hopefully Vectoria will slow down enough next time so Math Man can get that selfie with her.

The Problem this fortnight is to help Math Man figure out how to show BD and AE are perpendicular.  Write your solution on a quadrilateral sheet of paper, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 on Friday, October 21.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Ben Thinkin, Professors Geo. Metrie and Al G. Bragh -- on your solution. Good luck and have fun!

Buffon's Pine Needle Problem

Off on a Tangent