Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 December 1, 2017 Vol. 16, No. 7
http://www.math.hope.edu/newsletter.html


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
 
Abstract:
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. 


Math in the News: Christmas gifts for math geeks


Okay, this isn't news, but just some helpful advice on what to get that math geek on your Christmas list. Anyone would appreciate the mug shown here, especially since it includes the name of your favorite fortnighly mathematical newsletter. Amazon has (as usual) too many math geeky gifts from which to choose on its website. Choices include numerous mugs, t-shirts and a set of "the proof is in the pudding bowls."

Esty has a site devoted to gifts for math lovers that includes quadratic formula cufflinks, mathlete t-shirts, and golden ratio rings. Head over to Zazzle for prime number mugs, math symbol ties, and math formula night lights. Finally, you can pop across the pond to U.K.'s Maths Gear where you can find a hyperbola clock, torus balloons, and those ever-popular binary birthday candles.

Remember it is only (the number of partitions of 8)-days until Christmas!

Problem Solvers of the Fortnight

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

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.

Congratulations to the following students that submitted correct solutions:  Jeremiah Casterline, Christian Erickson, Ce Gao, Olivia Garcia, Hunter Gieswein, Jack Heideman, Russell Houpt, Karthik Karyamapudi, Noah Kochanski, Philip LaPorte. Nick Lillrose, Deb Nischik, Sarah O'Mara, Alex Osterbaan, Ashley Panton, Drew Pawlanta, Ben Shumaker, Andrew Smyk, Alex Sobczynski, Ryan Storteboom, Caleb Stukey, Caleb Sword, Hugh Thiel, Autumn VanVuren, Jincheng Yang, Yizhe Zhang, Will Zywicki


Problem of the Fortnight


A light bulb at point B on the vertical line x = -2 illuminates a region that is partially occluded by an arc of the circle x2 + y2 = 1.  How high must the light bulb be if the point (1.25, 0) is on the edge of the illuminated region?  (Click on the picture to the left to see an enlarged picture of this situation.)

Write your solution -- showing all your work, please! -- on a shadow and drop it by the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 p.m. on Friday, December 8.  As always, be sure to include your name and the name(s) of your professor(s) -- e.g. Slip Ray Slope, Dr. Al Luminate -- on your solution.


Little things make big things happen.

John Wooden

Off on a Tangent