|Off on a Tangent
|A Fortnightly Electronic
Newsletter from the Hope College Department of Mathematics
|October 20, 2017||Vol. 16, No. 4
|Next week's colloquium will again feature student research|
|Title: Student research presentations|
|Speaker: Mark Powers and Keri Haddrill|
|Time: Tuesday, October 24 at
|Place: VanderWerf 102
be holding practice sessions for the MATH Challenge mathematics
competition on Monday, October 23
and Monday, October 30
9:30 p.m. in 237 VanderWerf.
Please attend if you're interested in competing.
MATH Challenge will be held here at Hope on Saturday, November 4
a.m. to 12:30 p.m. This is an intercollegiate
regional competition. If you are interested
in participating, please let Prof. Cinzori (email@example.com) 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.
|Facebook Messenger now can interpret Latex Code|
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!
Solvers of the Fortnight
|In our last problem of the
had his workers move 69,489 crates.
The job took nine working days. Every day after the first day, he
put six more workers
on the job; and every day after the first day, each of the workers --
by arrangement -- shifted five fewer crates than was the quota for the
day before. The result was that, during the latter part of the
period, the number of crates being moved actually began to go down."
What was the largest number of crates moved on any one day?
Congratulations to all those that gave correct solutions: Jincheng Yang, Philip LaPorte, Zheng Qu, Russell Houpt, Andrew Nguyen, Alex Osterbaan, Caleb Stuckey, Yizhe Zhang, Nicholas Lillrose and Karthik Karyamapudi.
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.
on a Tangent