## Off on a Tangent 17.6

It is that time of year. No, not final exams, Christmas shopping. But what do you get the math geek on your Christmas list this year? To help you out, Business Insider made a list of some awesome gifts that include a Klein Bottle bottle opener, a telescope for your iPhone, chocolate gaming dice, and math joke t-shirts.

Esty also has a site devoted to gifts for math lovers that includes a Merry X-Math sweatshirt, pi ornaments, and some object that contains a hippopotenuse. (I guess that one is for those where only a hippopotenuse will do!) Head over to Zazzle for prime number mugs, math clocks, and lots of things that say something about math being importanter. (I’m not sure who would buy something like that!) Finally, if you take a trip over to Mathnasium you will find a cutie pi onesie, a hypercube paperweight, and pi cookie cutters.

Remember it is only (the smallest square that can be written as the sum of two squares)-days until Christmas!

## Problem Solvers of the Fortnight

Congratulations to Adair Cutler, Alyssa O’Donahue, Britta Johnson, Calvin Gentry, Camryn Zeller, Ce Gao, Chris McAuley, Christian Erickson, Dane Linsky, Dylan Burke, Ford Fishman, Hugh Thiel, Jacob Zoerhof, Jordan Corstange, Julia Loula, Kachikwu Nwike, Kam Wilcox, Karen Quay, Keegan Frisbie, Lydia Meinhard, Mackenzie Green, Mark Powers, Meredith Bomers, Micaela Wells, Mikaelah Snoap, Thomas Kouwe, Valerie Dien, Yizhe Zhang, Zach Wylie, Jonathan Washburn and Zheng Qu – all of whom correctly solved the Problem of the Fortnight in the last issue of America’s preeminent fortnightly mathematics department newsblog.

## Problem of the Fortnight

Positive integer n has the property that n – 64 is a perfect cube. Suppose that n is divisible by 37. What is the smallest possible value of n?

Write your solution (not just the answer) on a Christmas decoration of your own making, and drop it in the Problem of the Fortnight slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday, December 7. As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Carrie A. Toone, Professor Carol Ling – on your solution. Good luck and have fun!

## Graph Pebbling colloquium this week!

• Title: Graph Pebbling
• Speaker: Dr. Airat Bekmetjev, Hope College
• When/Where: 11 am on Thur, Nov 29 in VanderWerf 104
AbstractPebbling is a process defined on a connected graph. Pebbles are configured on vertices of the graph and are moved along the edges. A pebbling move consists of taking two pebbles from a vertex, placing one on an adjacent vertex, and discarding the other. The objective of pebbling is to put at least one pebble on a designated vertex, called the root. A configuration is called solvable if any vertex can get at least one pebble through a sequence of moves. Pebbling can be used in transportation and communication networks and optimal resource allocation.
Some interesting questions arise: How many pebbles are enough to guarantee that any configuration is solvable ? What are the optimal ways to move pebbles? Can we construct an algorithm that determines if a given pebbling configuration is solvable? In this colloquium we will try to answer some of these questions along with the discussion about the existence of the threshold phenomenon in pebbling. We will see how the solvability of a random pebbling configuration dramatically changes after the number of pebbles reaches a certain value called the pebbling threshold. We will also discuss new results in pebbling related to the two-pebbling property and Graham’s Conjecture on the product of graphs.

## The irrationality of pi will be presented in next week’s colloquium

• Title: Niven’s Proof of the Irrationality of Pi
• Speaker: Dr. Aaron Cinzori, Hope College
• When/Where: Tuesday, November 13, at 11:00 a.m. in VWF 102

Abstract:  Approximations of the value of pi are known to a ridiculous number of digits.  But to actually establish that pi is not a rational number requires not just approximations, but proof.  The first proof that pi is irrational was given by Lambert in 1761, and it required some sophisticated analysis, but in 1947, Ivan Niven gave a remarkably short and clear proof that pi is irrational using only ideas from calculus. (So it is as easy as pi!) We’ll take a detailed look at Niven’s proof as well as peeks at some of  the history of pi in mathematics.  And of course there will be poetry.

## Students participate in MATH Challenge

Hope again had a nice turnout of students participating in the Michigan Autumn Take-Home Challenge this past Saturday. Students competed with other students around the state (as well as other states) working in groups on ten interesting problems. Apparently this test was more difficult than usual (or not as easy as pi), so while we look forward to hearing the results in the near future we may not expect them to be very high scores. The following students competed (grouped by team):

• Chris McAuley, Quentin Couvelaire, Evan Bright
• Matt Edkins, Adam Czeranko, Mackenzie Green
• Evan Mulshine, Ruth Holloway, Trevor Hile
• Eric Leu, Jackson Krebsbach

## Memphis Teacher Residency

David Montague, the Director of the Memphis Teacher Residency (MTR), will be on campus next Wednesday, November 14th to speak in Chapel and recruit for MTR. He is also hosting an Information Session on that same day from 6:30-7:30pm in VNZ 247.

MTR provides a full year residency program preparing teachers for work in low-performing public schools in Memphis.  They offer a Master’s degree in Urban Education (tuition free), a full year internship co-teaching with a mentor teacher, free housing and a monthly living stipend.  Their mission is Christian love expressed in equal education.

## Problem Solvers of the Fortnight

Congratulations to Cole Persch, Evan Bright, Holly Denouden, and Caleb Stuckey– all of whom correctly solved the Problem of the Fortnight in the last issue of America’s premiere fortnightly mathematics department newsblog.

## Problem of the Fortnight

Consider the sequence a1 = 2, a2 = 3, a3 = 6, a4 = 18, . . . , where an = an-1 . an-2.  What is the largest k such that 3k divides a11?

Write your solution on a paper plate turkey (paper hand turkeys will also be accepted) and drop it in the Problem of the Fortnight Slot outside Professor Mark Pearson’s office, room 212 in The Werf, by 3:00 p.m. on Friday, November 16. We are hoping for a rafter of turkeys to appear in the Problem of the Fortnight slot next week! As always, be sure to include your name and the name(s) of your math professor(s) – e.g. Tom Gobbler, Professor Herb Stuffing – on your solution.  Good luck and have fun!