PCI Looking For Interns

PCI is a Norman based company that offers asset optimization solutions for power generation and trading companies. They are keen to hire people with a math background for internships. PCI is currently hiring for both regular and paid internship positions and will have Hiring Managers and different employees from different teams presenting and mingling with students after each session.

Date: Wednesday, September 23, 2015

Time:  10:30 am – 1 pm

Location: Frontier Room, 2nd Floor in Oklahoma Memorial Union Building


Pentagonal Tilings and Undergraduate Research

The new academic year is now well underway and the OU Math Club blog is back.  Behind the curtains, the role of blogmaster for the next year has been taken over by me, Jeff Meyer.  I am excited to tell you about all sorts of fun and interesting math things.  If you know of something that everybody should hear about, email me at jmeyer at math.ou.edu and we’ll get it on the blog!

As soon as I agreed to run the blog this year, I knew exactly what I wanted my first post to be about: tiling the plane. The idea is simple, namely what are the ways one can cover the whole plane by repeating some sort of geometric pattern?

One type of tiling requires you use only a single convex polygon over and over again.  (Recall a polygon is convex if its interior angles are less than 180 degrees.)  I suspect you can find a convex quadrilateral that you can use to tile the plane.  If you stretch or shear your quadrilateral a little bit, would it still tile the plane?  I encourage you to think about this, and maybe try sketching it one a piece of paper.  Sketching tilings is a fantastic way to pass the time in a boring meeting.

So let me now ask you a question: Can you find a single convex pentagon that will tile the plane?

It turns out, this is a really hard problem.

German mathematician Karl Reinhardt in 1918 first came up with 5 ways, and since then a total of 14 had been found. That is until this past year.  Three researchers at the University of Washington, Bothell found a 15th!  They found it after a lengthy computer search.  The algorithm for the search was developed by Dr. Casey Mann and Dr. Jennifer McLoud-Mann and automated by undergraduate David Von Derau.


All 15 known classes of pentagonal tilings, the bottom right being the one discovered by Mann, McLoud-Mann, and Von Derau. (EdPeggJr./Wikipedia)

It is amazing that there are so many open questions here:  Is this the complete list of convex pentagonal tilings? If not, are there finitely many?  Might there be infintiely many?

I think this is such a fantastic story for two reasons.  First, the problem is so easy to state and understand.  You could explain it to grade school students.  Second, this discovery was the result of a collaboration between faculty and an undergraduate.  For all you undergraduates out there, keep in mind there are lots of tangible research questions.  You just need to talk to some encouraging faculty who can help you find one.  If you do, then maybe next year there will be a post here about you!

Take a moment and check more details at the following links:



The Guardian:

University of Washington, Bothell:


John Nash: A beautiful mind now at rest.

It is with sadness that we report the loss of John Nash and his wife Alicia Nash in a tragic taxi accident.



Nash was featured in the movie, “A Beautiful Mind” that won 4 Oscars. The movie outlined his genius and his lifelong struggle with schizophrenia. Only last week he was in Norway to receive the prestigious Abel Prize.



Nash did extraordinary work in his field of partial differential equations and was a senior research mathematician at Princeton. He received the Nobel Prize in Economics in 1994 for his work in game theory. He was 86 years old; his wife was 82. You can find out more about Nash here:



The Queen of Code: Lt. Grace Murray Hopper

Have you heard the name Grace Hopper? The mathematical field of cryptography and theoretical computer science came of age during and after the Second World War. While the names of Turing, von Neumann and Godel are famous, and rightly so, history tends to forget or ignore the women who also played a critical part in these advances.

Lt. Grace Murray Hopper sitting at her desk. 1947 [?].

Lt. Grace Murray Hopper sitting at her desk. 1947 [?].

Here is a short film about one of the pioneers of computing, a woman who worked on the first computer, the Harvard Mark 1 and was part of the team that built the first compiler. The blog salutes Grace Hopper, the Queen of Code! Click below to see a short (about 16 minutes) documentary about her.


How often should you clean your room?

The blogmaster offers an unqualified apology for the absence. The end of the semester took its toll. But we are back with some mathematics!

Your own OU faculty members (Kimball Martin and Krishnan Shankar) have addressed the question that is in the title of this article in their paper:


but if you want the easier version here is a nice description in this blog:


Spoiler alert: mathematics proves that it pays to be a little lazy especially if you have a good memory!