Off on a Tangent 
A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics 
February 3, 2017  Vol. 15, No. 8 
http://www.math.hope.edu/newsletter.html 
Hope grad returns to present at next week's colloquium 
Title: Swarms of fireflies to restarting the heart: modeling the onset of synchrony  
Speaker: Dr. Mark Panaggio ’09, Assistant Professor of Mathematics, Hillsdale College  
Time: Tuesday, February 7 at 4 pm  
Place: VanderWerf 104 
Upcoming Colloquia 

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

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/ 
Statistics
Showcase 
The
15th annual Statistics Showcase, held on Friday, January 20, recognized
six outstanding student statistics projects of the Fall 2016 semester.
Congratulations go out to all of these students for their hard work and
outstanding results. The following projects were presented.

Euclidea is an app for geometric constructions 

If
you miss doing straightedge and compass drawings from your high
school geometry class, we found an app for you and you don't even need
a straightedge or compass. The site is called Euclidea and it can be accessed
on a computer or you can download a free app for your phone.
The authors state, "With Euclidea you don’t need to think about cleanness or accuracy of your drawing — Euclidea will do it for you. But it’s also a game. A game that values simplicity and mathematical beauty. Find the most elegant solution — the one, which is built in the least possible moves, — and you’ll get the highest score." 
Math in
Action 

Math in Action 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 hourlong sessions with eight separate
interactive presentations during each.
Last year the Math Department was able to fund the registration costs and provide transportation to the conference for interested Math Ed majors. We are making the trip this year and again the department will cover costs for our majors. In order to get the transportation request submitted in time, and to get the early bird registration rate, if you are interested in attending please let Dr. Mann know by Feb 7th. As payment is required when you register, Dr. Mann will be happy to do that for you and charge it to the department. The GVSU folks ask that you list a first and second choice for each session so that they can have a sense of rooms and resource needed. The brochure describes the choices for each session. What worked well last year was to have you fill out the first part of the registration form at the Math in Action website, print it and give it to Dr. Mann and he will take care of completing your registration. The keynote speaker is Tracy Zager who has a new book out, Becoming the Math Teacher you Wish You'd Had. You can preview the book here. 
Problem
Solvers of the Fortnight 

In
our last problem of the fortnight we saw the following exchange between
Math Man and Vectoria:
"Hi, Vectoria!" Looking
up from her table at Van Wylen, Vectoria says, "Oh, hi, Double M.
You seem chipper."
"Well,
I had a great Christmas break. I got caught up on some sleep over
the holidays, and I'm feeling rejuvenated at the start of this new
semester."
"Hey,
that's great. . . ." Vectoria's voice trails off as she turns her
attention back to the papers strewn out on the table before her.
"What are you looking at, Vectoria?" "Oh,
it's this problem I've been thinking about off and on for the past day
or two. The other day as I was sitting in the chapel, I looked up
at a stained glass window, and an interesting shape caught my
attention. It was a square, probably 2ft on each side. Two
quarter circles, centered at the lower vertices of the square,
intersected each other to form something like this," said Vectoria, as
she showed Math Man the picture she had drawn:
"Wow,
you draw really neat pictures, Vectoria!"
"Thanks,
M's. What I was wondering," Vectoria continued, "was whether I
could find the areas of the smaller regions in the square."
"Hmmm.
. . . Which region in particular?"
"Oh,
I don't know. Any of them, I suppose. I think once you
found one, you could probably get the others."
"Yeah,
maybe you're right. . . . It's kind of a cool problem. Can
I work on it with you?"
"Sure!
Which region should we tackle first, Double M?"
"How
about ABE?"
Congratulations
to Brandon Brown, Owen Donahoe, Richard Edwards, Jeffrey Engle, Jason
Gombas, Keri Haddrill, Philip LaPorte, Alex Osterbaan, Babu Bhatt,
Zheng Qu, Hugh Thiel, Joey Watson, Elizabeth Woodford, Jincheng Yang,
and YungChul Yoon  all of whom correctly solved the first P. Fort of
the new year!

Problem
of the Fortnight 

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." Help Math Man and Vectoria by proving that AP = BQ, explaining your reasoning clearly and carefully. Submit your solution to the Problem of the Fortnight slot outside Professor Mark Pearson's office by 3:00 p.m. on Friday, February 10. As always, be sure to include your name, as well as the name(s) of your math professor(s)  e.g. Noah Dia, Professors Les Schur and Rhea Lee  on your solution. Good luck and have fun! 
Off
on a Tangent 