Off on a Tangent 
A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics 
February 17, 2017  Vol. 15, No. 9 
http://www.math.hope.edu/newsletter.html 
Combined mathematics and engineering colloquium scheduled for next week 
Title: TBA  
Speaker: Dr. Seth Guikema  University of Michigan  
Time: Fri, Feb 24 at 3:00 PM  
Place: VanderWerf 102 
Upcoming Colloquia 

We have the following additional math colloquia
on the schedule for this semester. More will most likely be added.

Help
determine which talks are given on Pi Day! 
Dave
Kung from St. Mary's College of Maryland is our "Piday" speaker and he
will be giving two talks on that day (314). He has many interesting
talks up his sleeve and YOU have the opportunity to help him decide
which talks he will give. Go to the survey linked here to help Dave make
his decision. Also, you can get a preview of Dr. Kung in the following videos:

Students present at the Nebraska Conference for Undergraduate Women in Mathematics 

Two
Hope Students, one Hope professor, three GVSU students plus one
professor, and a student from Davenport University recently attended
the Nebraska Conference for Undergraduate Women in Mathematics (NCUWM).
Sarah Petersen gave a talk titled “Modeling Pioneer Plant Populations
in the Monteverde Cloud Forest,” which was based on research she did
with Brian Yurk and Greg Murray this past summer. Jiyi Jiang presented
a poster titled “Incorporating Information from Exogenous Variables in
Models for Disease Incidence,” which was based on research she has been
doing with Yew Meng Koh.
Highlights from the conference include talks and posters by undergraduates, a panel discussion on careers in mathematics, and opportunities to talk with mathematics students and professors from around the country. Sarah and Jiyi would encourage anyone interested in attending the conference next year to contact either them or Professor Edwards for more information. Jessalyn Bolkema, a 2012 Hope mathematics graduate and current graduate student at the University of Nebraska, was also attending the conference and met up with the Hope group shown in the picture on the left. 
Lower Michigan Mathematics Competition 

The 41st Annual Lower Michigan Mathematics Competition
(LMMC) will be held at UMFlint 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 cinzori@hope.edu. 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, Statistics and Electrical Engineering &
Computer Science departments are running a sixweek 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 1, 2017. For more information about the workshop and an application visit https://sph.umich.edu/bdsi/ 
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: On her way through Van Wylen Library, Vectoria spots Math Man sitting on a table, deep in thought. "Hey, M's. What'cha doin'?" "Well, I was trying to figure out this math problem: If r_{1} and r_{2} are the roots of x^{2} + bx + c = 0, then the sum of the roots is b and the product of the roots is c. Why is that?" "Oh, well, if r_{1} and r_{2} are the roots of the x^{2} + bx + c, then it must factor as (x  r_{1})(x  r_{2}), which multiplies out to x^{2}  (r_{1} + r_{2})x + r_{1}r_{2},
and since
this has to be equal to x^{2} + bx + c, we need (r_{1} + r_{2}) = b and r_{1}r_{2} = c.""Oh, that's cool! I didn't know that." "Yeah, it's kind of interesting, I guess. But why did you want to know that, Double M?" "Oh, I don't really. It's just a hint that Professor Airat Bekmetjev gave me for the problem I'm really interested in." "Airat Bekmetjev. . . . What kind of a name is that?" "I don't know. I think maybe it's Dutch." "Hmmm. . . . Anyway, what's the other problem you're working on?" "Oh, it's kind of cool. A line intersects the hyperbola xy = 1 at points P and Q and the xaxis at A and the yaxis at B. The problem is to prove that AP = BQ" "Wait! Any line?" "Yeah, I guess so. It just says 'a line,' so I'm assuming it means any line that intersects the curve in two points and also the x and yaxes." "And what about P and Q? Do they have to be in any particular positions?" "No, I don't think so. It just says they are points where the line intersects the hyperbola. I think they could be either like this . . . or like this," Math Man says, showing Vectoria the figures he's drawn. "Hmmm. . . . That is kind of a cool problem. But how does Dr. B's hint help?" "I don't know. That's what I'm trying to figure out." Congratulations to Philip LaPorte, Zheng Qu, and Jincheng Yang  all of whom correctly solved the Problem of the Fortnight in the last issue of America's alreadygreat fortnightly electronic mathematics department newsletter. 
Problem
of the Fortnight 

"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 357 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 trimendous coincidence!" "What?!" "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. . . ." "M's?" "Right. Sorry. The problem is to figure out a^{2} + b^{2} + c^{2}." Write your solution on a scalene triangle 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, February 25. As always, be sure to include your name, as well as the name(s) of your math professor(s)  e.g. Ivan Idea, Professor Juan der Er  on your solution. 
Off
on a Tangent 