Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 November 17, 2017 Vol. 16, No. 6

Acoustical engineer will speak at next week's colloquium

Title: Computational AeroAcoustics: Prediction of Noise from a simple fan system using Computational Fluid Dynamics (CDF) Systems
Speaker:  Dr.  Peter Laux
Time:  Tuesday, November 21 at 11:00 am
Place:  VanderWerf 102
Presented is an approach to define an analysis process, where the goal is to accurately and easily predict the noises generated by a simple fan during operation (at load). Prediction of flow noise requires the utilization of computational fluid dynamics tools and the merits of two basic approaches (fundamental equations) are explored as well as the adaptation of test methods to accommodate some of the inherent limitations in the tools.

The battle between mathematics and truth will take place after Thanksgiving

Title: Battle of the Titans: Mathematics vs Truth
Speaker:  Dr. Tim Pennings, Davenport University
Time:  Thursday, November 30 at 11:00 am
Place:  VanderWerf 102
What is Truth?  This question asked by Pontius Pilate at Jesus's trail has haunted reflective people for centuries. Supreme Court Justice Potter Steward said of pornography (roughly): I can't define it, but I know it when I see it. Similarly, epistomologists (and others who study truth and our ability to know truth) have used mathematics as a proof for the existence of truth. Does truth exist? Yes, consider mathematics. What is truth? Consider mathematics.

But now the soft underbelly of mathematics has been exposed, showing that mathematics - and the world of Truth - is much richer and darker than ever imagined. Come explore the world of alternative facts. Not for the faint-of-heart.

The final colloquium of the semester will look at the impossible

Title: Integration in Finite Terms: Possible, Impossible, and How We Know
Speaker:  Dr. Dave Gaebler, Hillsdale College
Time:  Tuesday, December 5 at 4:00 pm
Place:  VanderWerf 102
You've probably heard, as part of the mathematical lore, that certain functions like e^{x^2} are impossible to integrate.  But what exactly does that mean?  And how do we know it's not just really hard?  With some perspective from abstract algebra (no prior knowledge required), we will consider the nature of impossibility proofs, the theory-building required to attain them, and the particulars of the theory needed to settle the integrability question. 

Hope students participate in the MATH Challenge

Hope again had a great turnout of students participating in the Michigan Autumn Take-Home Challenge on November 4 this year.
Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. The problems included Alice and Betty playing a game on a 3 by n checkerboard, finding the 2017th derivative of a function, and a creative way to transform one fraction into another. We look forward to hearing the results in the near future.

The following students competed (grouped by team):
  • Zheng Qu, Yizhe Zhang, Jincheng Yang
  • Calvin Gentry, George Becker Rust, Cole Persch
  • Dane Linsky, Luke Christensen, Thomas Kouwe
  • Lindsey Hoaglund, Yong Chul Yoon
  • Philip LaPorte, Andrew Nguyen
  • Karthik Karyamapudi, Sam VanderArk
  • Jeffrey Engle, Joseph Watson, Blake Harlow

Mathematical Competitive Game

If you have some free time over this coming Thanksgiving break or Semester break and like mathematical competitions, we have one for you of international proportions. The Mathematical Competitive Game 2017-2018 sponsored by the Fédération Française des Jeux Mathématiques (French Federation of Mathematical Games) and Société de Calcul Mathématique SA (Mathematical Modeling Company) is currently in progress.

This competition is on the distribution of goods. In particular, they have a company that manufactures heaters and air conditioners and needs help in the mathematics behind production and distribution. You can write your solution up in either English or French!

Problem Solvers of the Fortnight

In our previous problem of the fortnight we had the following:

Starting with the vertices of a square, P1 = (0,1), P2 = (1,1), P3 = (1,0), P4 = (0,0), we construct the following points as shown in the figure on the right (click on the figure to enlarge it).  In the figure, P5 is the midpoint of the line segment P1P2, P6 is the midpoint of the line segment 
P2P3, etc.  The infinite sequence of points P1, P2, P3, P4, P5, P6, P7, ... approaches a point P inside the square.
  1. If the coordinates of Pn are (xn, yn), find xn and yn for 1 < n < 13.
  2. Show that (1/2) xn + xn+1 + xn+2 + xn+3 = 2 for 1 < n < 9.  Find a similar formula for the y-coordinates and show that it is true for 1 < n < 9.
  3. Find the coordinates of P.
Congratulations to the following students that submitted correct solutions:  Daniel Clyde, Christian Forester, Keri Haddrill, Grace Kunkel, Philip LaPorte, Caleb Stukey, and Alyssa VanZanten

Problem of the Fortnight

The line y = x + 6 intersects the parabola y = x2 at points A and C in the figure shown on the left.  (You can click on the figure to enlarge it.)  Find the point B on the arc of the parabola between A and C that maximizes the area of the triangle ABC.

Write your solution -- showing all your work, please! -- then stuff it into a turkey and drop it by the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 p.m. on Monday, November 27 (right after the Thanksgiving break).  As always, be sure to include your name and the name(s) of your professor(s) -- e.g. Max E. Mum, Dr. Mini Mize -- on your solution.

Be thankful for what you have; you'll end up having more. If you concentrate on what you don't have, you will never, ever have enough.

Oprah Winfrey

Off on a Tangent