Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 September 14, 2015 Vol. 14, No. 1

Hope Students present at upcoming colloquium 

Titles:  A) Level Curves of a Real Algebraic Function: A Generalization of a Theorem of Pólya
              B) Predicting Transitions in Bean Beetle Embryo Development Using Wavelet Transforms and Neural Networks
Speakers:  Sarah Hilsman, Anna Snyder and Zach Diener
Time:  Tuesday, September 22 at 4:00 pm
Place:  Schaap Science Center 1118

Abstracts: (A) We consider an old theorem of George Pólya's which looks at the level curves of certain polynomial functions and the intersection of such curves with lines of positive slope. We extend Pólya's theorem, relaxing conditions on the polynomial functions and considering intersections with lines of negative slope. The degree two case gives us hyperbolic paraboloids, leading to a brief visual demonstration of solid analytic geometry (the algebraic study of the real vector space R3).

(B) As bean beetle embryos develop, time-lapse photographs of their eggs exhibit varying levels of brightness that correspond to different stages of maturation. These time signals can be analyzed to pinpoint when different stages of development occur. These stages are marked by transitions in the time signal, for which we have developed a method to accurately identify and predict. Wavelet transforms are utilized to analyze the signal over various time windows in order to identify features of varying scales within the signal. Key features are then extracted from the wavelet analysis in order to use as inputs to a neural network, which will automate the process of identifying and predicting the points of transition. We have studied this method’s accuracy at various levels of noise using simulated data based off lab data.

Hope Student Receives Prestigious Mathematics Education Scholarship

The 2015 National Council of Teachers of Mathematics Prospective 7-12 Secondary Teacher Course Work Scholarship was awarded this past summer to Grace Wiesner. After going through an extensive application process, Grace received the maximum award of $10,000 for her outstanding academic scholarship and research pursuits. 

Hope students earn Outstanding Speaker Awards

Four Hope College Mathematics students won Outstanding Speaker Awards at the Mathematical Association of America’s annual national conference, MathFest, this past summer.  Sarah Hilsman (Real algebraic level curves), Anna Snyder (An extension of a theorem of Polya), and Cole Watson (Graph pebbling and Graham’s conjecture) all won prizes from Pi Mu Epsilon, the national mathematics honorary society and Jiyi Jiang (Classify images using stochastic neighbor embedding and mapper) won an award from the MAA. 

All four of these students participated in research this summer under the direction of Stephanie Edwards, Chuck Cusack, and Paul Pearson. See below for some pictures of their excursion to Washington, DC for MathFest.

Ice Cream and Fun

Please join the mathematics faculty and fellow math students for the Ice Cream and Fun event on Friday, September 18 from 3:14 to 4:14 p.m. (that's pi time to pi+1 time)  We will set up in the Van Andel Plaza located in front of the Schaap Science Center. (We will use the Science Center Atrium in case of rain). Come and enjoy delicious ice cream, some fun games, and get to know your fellow math students and faculty.

Hope to see you there!

New Science and Mathematics Education Student Group Forming

A new group of science and mathematics education students called Sci-pi is forming. The first meeting is Tuesday, September 15 from 5-6 p.m. in VanZoeren 247 with pizza and pop provided.

This new student organization will:
  • Learn about and share high quality science and mathematics teaching resources
  • Volunteer for science and mathematics outreach activities in local K-12 schools
  • Go on field trips to local resource hubs for science and math teachers, such as the Outdoor Discovery Center and the GVSU Regional Math and Science Center
  • Hear expert guest speakers talk about current practices in K-12 mathematics and science
  • Network with peers who will be teaching in the same fields
  • Plan involvement in Professional Organizations including NSTA and NCTM
If you have questions, contact Dr. Vicki-Lynn Holmes ( or Ms. Carrie Dummer (

Math Club

  • Math Club will be having lunch at Phelps every Thursday at 11:30 this semester beginning September 24th.  Please join us as you are able.
  • The first meeting of Math Club will be at 7:00 p.m. on Monday, September 21 in the atrium of the Schaap Science Center.  This first meeting will be largely social and informational, but we'll also work on the Problem of the Fortnight a little bit. 

UN World Statistics Day Data Visualization Challenge

As part of the celebration of World Statistics Day (WSD) on October 20 and following the release of the Millennium Development Goals (MDG) Report by the United Nations, the United Nations Statistics Division has announced the #WSD2015 Data Visualization Challenge competition.  The challenge is to build an infographic or dynamic visualization featuring the latest data from the 2015 MDG report.  Data and submission guidelines can be found on the WSD2015 Data Visualization Challenge website.  If you are interested in working on this with a team of up to three people, please email Paul Pearson well in advance of the submission deadline (September 20). We may have more that one team from Hope College, so the more the merrier!

Math in the News: Hinged Flat Torus

A little more complicated than a Cheerio or a doughnut, Henry Segerman, an Oklahoma State University mathematics professor, has developed a hinged flat torus. (We had an article last year in Off on a Tangent 13.6 about Segerman's Pumpkin Geometry.) Segerman created a torus (the shape of a doughnut) that can be unfolded so that it results in a flat shape. He's kind of messing with topology a bit here.

You can see a video of the hinged flat torus and even purchase one for that special mathematician on your Christmas list here.

Problem of the Fortnight

In the triangle shown on the left, BD/DA = 1/2, CE/EB = 1/4, and DG is parallel to BC.  Find CF/FD.

Write your solution on a triangular piece of paper and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Wednesday, September 23.  As always, be sure to write your name and the name(s) of your math professor(s) -- e.g. R.U. Shurr, Professor S.I. Yam -- on your solution.  And remember -- the Math Club will be meeting at 7:00 p.m. on Monday, September 21 to work on the problem, so if you haven't solved it by then, please join them to try and figure it out!

Off on a Tangent