Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 September 22, 2017 Vol. 16, No. 2

Next week's colloquium will feature Zeno's Paradox and more!

Title: Zeno’s paradox, the harmonic series, and ½ = 1???
Speaker:  Dr. Stephanie Edwards
Time:  Tuesday, September 26 at 4:00 pm
Place:  VanderWerf 102

Abstract: Zeno’s paradox says that before one can get to position A, one must first get half way there. Before one can get to the halfway point, one must get half way to the halfway point, and so on.  Since this goes on forever, it seems that the distance cannot be covered.  We will use geometric series to show that the distance will, indeed, be covered.  We will also explore the harmonic series and show that rearrangements of the alternating harmonic series can lead to puzzling conclusions.

Putnam and MATH Challenge


Two mathematics competitions that take place each fall are the MATH Challenge and the Putnam Exam.  Students can compete in either of these competitions without leaving Hope's campus.  Information about each of these follows.

The MATH Challenge

The 2017 Michigan Autumn Take Home Challenge (or MATH Challenge) will, most likely, take place on the morning of Saturday, November 4 this year. (More information will be in a future newsletter once this date can be confirmed.) Teams of two or three students take a three-hour exam consisting of ten interesting problems dealing with topics and concepts found in the undergraduate mathematics curriculum.  Each team takes the exam at their home campus under the supervision of a faculty advisor. 

The department pays the registration fee for each team and will provide lunch to participants afterwards. A group of students may sign up as a team.  Individual students are also encourage to sign up; they will be assigned to a team on the day of the competition.  For more information, please talk with any member of the Mathematics Department or visit the MATH Challenge website
where you can also view old copies of the exam. 

The Putnam Exam

The William Lowell Putnam Mathematical Competition, administered by the Mathematical Association of America, is the most prestigious mathematical competition for undergraduates in the nation.  If you are interested in taking the Putnam Exam, you must email Professor Cinzori at by Friday, October 6 (right before Fall Break).  The date of the exam is Saturday, December 2. There is both a morning (10am - 1pm) and an afternoon (3 - 6pm) session of this exam.  Participants need to be there for both sessions.
 Lunch will be provided by the mathematics department during the break.  For more information about the Putnam Exam visit the website.

Chuck Cusack will show his mathematical art at ArtPrize this year

Chuck Cusack, a member of both the Mathematics Department and Computer Science Department at Hope College, will be competing in ArtPrize once again this year.  He creates mathematical art out of Lego bricks.  His entry this year, Squares, is a collection of squares made out of Lego bricks mostly consisting of Latin squares. 

You can read more about his here and you can see many pictures of this and his other mathematical Lego art on his Instagram page and his Facebook page.

History of the equals sign

There was an interesting article in Ars Technica this past summer about the origin of the equals sign. It is hard to imagine doing mathematics without it, but as you know, someone had to invent it before we could use it. About 500 years ago, a Welshman named Robert Recorde invented the sign and was the first to use a few more things (like English instead of Latin) to make mathematics easier to understand.

Read more about this interesting story titled, "The strange and righteous history of the equals sign" where you will also learn that Recorde did not live out his life as a mathematical hero. He instead clashed with an Earl and that led to his ultimate demise.

Ice Cream and Fun

At last week's math social, a super fun mixer game was played. The participants answered  a short series of multiple-choice questions, like, "If you had a super power, what would it be?" They then had to find others that had the same answers for all the questions or others that had no answers in common. A couple of the winning groups are shown.

After that, everyone enjoyed ice cream with fabulous toppings. The weather was perfect for enjoying the dessert and socializing with other students and faculty!

The event also inspired the problem of the fortnight shown below.

Actuarial Career Opportunity Day

Auto-Owners invites you to their annual Information Technology & Actuarial Career Opportunity Day! The event is on Friday, October 20, 2017 from 10:30 a.m. to 4:00 p.m. IT/Actuarial Day shows students how their degree can be used in the insurance industry.
Sophomores, juniors, seniors, and recent graduates with majors in Mathematics and Computer Science are invited. Faculty is also welcome! Each faculty member who wishes to attend should fill out a registration to ensure we adequately prepare for the correct number of attendees.

More information and registration should be available soon and will hopefully be in the next newsletter.



Biostatistics Prospective Student Information Day

The Department of Biostatistics at the University of Michigan will hold a Prospective Student Information Day on Saturday, September 30, 2017. The purpose of this event is to provide information to students who may be interested in graduate study in biostatistics. They expect attendees to be undergraduate and masters students who have identified biostatistics as their interest area, as well as students who are completing an undergraduate degree in math, statistics, biology, or some related discipline, and have not yet decided on their future plans.

At the event, presentations by students and faculty will focus on what biostatistics is and what biostatisticians do, on the job opportunities in biostatistics, and on the admissions and financial support opportunities at the University.

For more information, please visit their website (where you can also register).

Problem Solvers of the Fortnight

In our last problem of the Fortnight, we let A = (a,a2) and B = (b,b2) be two points on the graph of the parabola y = x2 such that the tangent lines to the parabola through A and B are perpendicular.  Let C be the point where the tangent lines meet at a right angle.  Find the x- and y-coordinates of the point C in terms of a.

There were a couple of solutions that were submitted, appropriately so, on parabaloids. One is picture here.

Congratulations to Jacob Conroy, Matthew Dickerson, Calvin Gentry, Keri Haddrill, Karthik, Karyamapudi, Philip LaPorte, Kenneth Munyuza, Andrew Nguyen, Sarah O'Mora, Alex Osterbaan, Zheng Qu, Forest Rulison, Hugh Thiel, Jincheng Yang, Yizhe Zhang for correctly solving this problem!

Problem of the Fortnight

To help keep you cool on these unseasonably-warm days, we are giving you an ice cream cone for a problem of the fortnight!

In the figure shown, the blue triangle POQ is isosceles since sides OP and OQ both have length 4, theta is the angle POQ at the bottom of the triangle, and a pink semicircle sits atop the isosceles triangle.  
  • Find the area of triangle POQ as a function of theta.
  • Find the area of the semicircle as a function of theta.
  • Find the limit as theta goes to 0 of the ratio of the area of the triangle to the area of the semicircle.
Put your solution (not just the answer) in an ice cream cone and submit it to the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 p.m. on Friday, September 29.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Ethan Almond, Dr. Cherry Garcia -- on your solution.

Don't just aspire to make a living; aspire to make a difference.

Denzel Washington

Off on a Tangent