Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
April 15, 2016 Vol. 14, No. 13

A history lesson in proportion estimation will be the topic of next week's colloquium

Title: Of Poohsticks, P-values, and Plus-Four: A Perambulation through a Century of Inference for Proportions
Speaker: Eric Nordmoe, Kalamazoo College
Time:  Tuesday, April 19 at 4:00pm
Place:  VanderWerf 102

Bernie or Hillary? Coke or Pepsi? Punt or go for it? Ted or Donald? These and many other questions of interest present the problem of estimating a proportion parameter for some population of interest. How serendipitous that A. A. Milne’s Bear of Very Little Brain faced this problem nearly a century ago, just three years and a hundred or so kilometers removed from the birthplace of R. A. Fisher’s Statistical Methods for Research Workers, the classic book in which the term “test of significance” was first coined! Suitably inspired, we will survey both early and modern approaches to inference for proportions.  Particular attention will be paid to a shocking discovery that led statistics educators to overhaul classical methods taught for calculating confidence intervals for proportions.

Student's travel to mathematics conference

Saturday, April 2nd, Rachel Alfond, Daria Soloman, Anna Dlugosz, Russel Houpt, Kade Steffes, Sarah Petersen, Kristen Pogats, Megan Klintworth, Hannah Howard, Professor Stephanie Edwards, and Professor Paul Pearson traveled to Hillsdale College for the 2016 Annual Michigan Section of the MAA and Michigan Undergraduate Mathematics Conference.

The conference consisted of plenary talks regarding the study and research of embodied cognition and a ring homomorphism technique in algebraic geometry to understand complex algebraic varieties. Among many other talks presenting research, Hope College’s Professor Paul Pearson shared his techniques of teaching linear algebra using representative grids and commutative diagrams. As the day ended— friendships grew, math ruled, and the question: “Would it even be possible for Professor Edwards to effectively teach with her hands tied behind her back?” was debated.

Students excel in actuary program

As we are approaching the end of the academic year, we want to commend some of our students pursuing a careers in actuarial science. The professional growth in this career depends on passing national actuarial exams that cover such topics as probability theory, financial mathematics, stock markets and many more areas related to mathematics and economics. Hope College Department of Mathematics offers courses and independent study to prepare students for some of these exams.

This year we want to mention names of Paul Nelson, who already passed three actuarial exams and was offered a position in an actuarial company in Illinois, Tyler Valicevic who passed two exams and is planning on working in an actuarial company in Michigan after graduation and recent Hope graduate Tae Hyun Choi who passed two exams and was accepted to the graduate school in Statistics at the University of Waterloo. Congratulations and best wishes!

For more information on the actuary profession visit

Math in the News: Andrew Wiles to receive Abel Prize

Oxford professor Andrew Wiles was recently awarded the Abel Prize “for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory.” The prize also comes with a check for 6,000,000 Norwegian Kroner or a bit over $700,000.

Fermat's Last Theorem states that there are no whole number solutions to the equation xn + yn = zn when n is greater than 2. Pierre de Fermat, a 17th century mathematician, claimed to have a proof but none was ever found.

According to a recent article in The Telegraph, Wiles said, "Fermat's equation was my passion from an early age, and solving it gave me an overwhelming sense of fulfillment." Wiles worked for years on the proof for years by himself while he was at the Princeton University and completed his proof in 1994.

The Abel Prize is sometimes called the "The Mathematicians' Nobel" and is named after Norwegian mathematician Niels Abel.

Problem Solvers of the Fortnight

In our last POTF we gave the following problem:

The line y = mx, where m > 0, forms an acute angle with the x-axis, and the point P = (a,b) lies in the interior of the angle.  A line through P intersects both the x-axis and the line y = mx to form a triangle.

What is the minimum area of this triangle?  Express your answer in terms of m, a, and b.

Congratulations to Zac Geschwendt and Jesse Ickes, both of whom correctly solved the last Problem of the Fortnight.

Problem of the Fortnight

A light bulb is located at the top of the pole in the figure.  How tall must the pole be if the point (1.25, 0) is right on the edge of the illuminated region? (And yes, that is a blue semicircle  of radius 1 centered at the origin in the drawing.)

Write your solution on a semicircular piece of paper and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson's office (VWF 212) by 3:00 on Friday, April 22.  As always, be sure to include your name and the name(s) of your math professor(s) -- e.g. Justin Thyme, Professor Ty M. Lee -- on your solution.  Good luck and have fun!

However impenetrable it seems, if you don't try it, then you can never do it.

Andrew Wiles

Off on a Tangent