Off on a Tangent 
A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics 
October 20, 2017  Vol. 16, No. 4 
http://www.math.hope.edu/newsletter.html 
Next week's colloquium will again feature student research 
Title: Student research presentations  
Speaker: Mark Powers and Keri Haddrill  
Time: Tuesday, October 24 at
4:00 pm 

Place: VanderWerf 102 
MATH
Challenge 
We'll
be holding practice sessions for the MATH Challenge mathematics
competition on Monday, October 23
and Monday, October 30
from 8:00
to
9:30 p.m. in 237 VanderWerf.
Please attend if you're interested in competing. The
MATH Challenge will be held here at Hope on Saturday, November 4
from 9:30
a.m. to 12:30 p.m. This is an intercollegiate
regional competition. If you are interested
in participating, please let Prof. Cinzori (cinzori@hope.edu) know by Tuesday,
October 24. You can sign up with your friends
as a team of up to three people, or you can sign up as an individual
and be placed on a team. More details in Off
on a Tangent. You can find some recent competition problems here, here, and here, and links to more in the sidebar here.


Facebook Messenger now can interpret Latex Code 

Latex
is a typesetting system that most mathematicians use to write papers,
books, and your calculus quizzes. It is used so much because it allows
the user to produce nicely typeset mathematical equations as well as
other mathematical objects like matrices. Now you can communicate with your favorite mathematician using Latex code in Facebook Messenger. It does come with some limitations. It only works on the desktop version, not your phone, you need double dollar signs around your text, and the entire message has to be in Latex, not just part of it. Give it a try! 
Problem
Solvers of the Fortnight 
Problem
of the Fortnight 
A red circle is
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?
Write your solution (showing all relevant work) on the back of a twenty dollar bill and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Friday, October 27. As always, be sure to include your name and the name(s) of your math professor(s)  e.g. Hope Anna Prayer, Professor Wacław Sierpiński  on your solution. 

Figure 1 
Figure 2 
Figure 3 
Off
on a Tangent 