Off on a Tangent 
A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics 
November 3, 2017  Vol. 16, No. 5 
http://www.math.hope.edu/newsletter.html 
Cryptograph will be the topic of next week's colloquium 
Title: The Mathematics of Secrecy: A Brief Introduction to Cryptography  
Speaker: Dr. Charles Cusack  
Time: Thursday, November 9 at
4:00 pm 

Place: VanderWerf 102 
You can’t tell a gerrymandered district by its shape 

Gerrymandering,
the process to select political districts so that to make it
advantageous to a certain political party, is a hot topic these
days. In the past few months, there have been petitions widely
distributed in Michigan to get a ballot proposal to end the practice. But how do you tell if the boarders of a Congressional district have been determined through gerrymandering? Can you tell by its shape? According to a couple of mathematicians, the answer is no. The pair recently published a paper on this topic. You can read more about this in the Ohio State News and Dustin Mixon's blog. You can also read there paper here. 
Problem
Solvers of the Fortnight 
In our last problem
of the fortnight we had a red circle inscribed in an equilateral
triangle of side length w (see Figure
1). In each of the three corners of this triangle, a smaller
equilateral triangle is drawn tangent to the red circle, and a cyan
circle is inscribed in this smaller triangle (see Figure 2). The
next step in this process is shown in Figure 3. If this process
of drawing smaller equilateral triangles with inscribed circles is
continued indefinitely, what is the total area of all of the circles in
terms of w?
Congratulations to Kevin Catalfano, Philip LaPorte, Nick Lillrose, Dane Linsky, Andrew Nguyen, Alex Osterbaan, Eleda Plouch, Sam VanderArk, and Eildert Zwart for submitting correct solutions. 

Figure 1 
Figure 2 
Figure 3 
Problem
of the Fortnight 
Off
on a Tangent 