Off on a Tangent 
A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics 
October 14, 2016  Vol. 15, No. 3 
http://www.math.hope.edu/newsletter.html 
Annual Gentile Lectures will feature a computational mathematics scholar 
Title: History of Computing
and Its Role in Society Time: 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 
Upcoming Colloquia 

The following additional colloquium is on
the
schedule
for this semester, but more should be added.

Interview with Aaron Green 
Students
present at mathematics education conference 
Professors Jane Finn and
VickiLynn 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! 