# FAMUS

The “Friday Afternoon Mathematics Undergraduate Seminar” (FAMUS) is a weekly event consisting of announcements, talks, and faculty interviews. FAMUS takes place most Fridays at 3:00-4:00pm in Room 164 of the Adel Mathematics Building. Typically the first half of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half. FAMUS is hosted by Jeff Rushall.

Come join us for some entertaining talks! Refreshments always served.

# Schedule Fall 2021

Note that talks are listed in reverse chronological order.

### Euler Bricks

Date: Friday, November 19

Speaker: Jeff Rushall (NAU)

Abstract: This talk will present an overview of the search for both Euler Bricks (3-D blocks whose dimensions and face diagonals are integers) and perfect cuboids (Euler Bricks whose internal diagonal is also an integer).

Come for the math, stay for the drama and free candy. The faculty guest this week is Sarah Watson. [PDF of Flyer]

### The Tree of Pythagorean Triples (and Quadruples)

Date: Friday, November 12

Speaker: Jeff Rushall (NAU)

Abstract: This talk will explain a cute way to depict all primitive Pythagorean triples as the vertices of a rooted perfect ternary tree. I will also explain a NOT cute way to depict all primitive Pythagorean quadruples (but the method found led to two NAU undergrads, Marcela Guttierez and Viola McCarty, getting published!).

The faculty guest will be David Deville. [PDF of Flyer]

### $\pi$

Date: Friday, November 5

Speaker: Jeff Rushall (NAU)

Abstract: You all probably know what $\pi$ is (that geometry constant thingee). But you might not know how it is computed, or who computed it when, or alternative ways to describe its value. These and more will be discussed at FAMUS. In addition to discussing pi, we will EAT pie. There will be at least 4 pies served. Honest! Come for the pi, stay for the pie.

It will be a short-ish FAMUS (no faculty guest this week). We’ll eat pie while we learn about pi, and then the weekend begins. [PDF of Flyer]

### Amicable Pairs

Date: Friday, October 29

Speaker: Jeff Rushall (NAU)

Abstract: Amicable pairs are pairs of whole numbers believed to share a mystical connection (according to the Ancient Greeks). One such pair is on the attached poster! I’ll present a brief history of amicable pairs, show you how to find a few, and state some questions about amicable pairs that do not yet have answers.

The faculty guest will be Rachel Neville. [PDF of Flyer]

### Turan’s Brick Factory Problem

Date: Friday, October 22

Speaker: Jeff Rushall (NAU)

Abstract: During World War II, Hungarian mathematician Paul Turan, being Jewish, was forced to work in labor camps. At one of these camps - a brick factory - he encountered a situation that led to a new mathematical idea and lots of subsequent research in graph theory. Come for the drama, stay for the math and free candy.

The faculty guest will be Ian Williams. [PDF of Flyer]

### Ramanujan

Date: Friday, October 15

Speaker: Jeff Rushall (NAU)

Abstract: The talk will delve into Ramanujan’s mysterious life and his even more mysterious mathematics. I’ll do my best to show some of his more amazing formulas.

The faculty guest will be Ellie Blair. [PDF of Flyer]

### Cantor Sets, Sierpinski Carpets and Menger Sponges

Date: Friday, October 8

Speaker: Jeff Rushall (NAU)

Abstract: Is it possible for a 3-D object to have finite volume but infinite surface area? The answer is YES. We will talk about such an object, along with 2-D and 1-D versions of the same counterintuitive beast. We will also see pictures of egg dishes and cookies that are inspired by the same ideas.

The faculty guest will be Shannon Guerrero. [PDF of Flyer]

### The Shoelacing Counting Problem

Date: Friday, October 1

Speaker: Jeff Rushall (NAU)

Abstract: There are MANY different ways to lace up shoes. After explaining the rules associated with “lacing up” a pair of shoes, we will see how many ways there are to lace up shoes. No prior knowledge of shoe lacing is required.

The faculty guest will be Tyler Brock. [PDF of Flyer]

### Tragic Deaths in Mathematics History

Date: Friday, September 24

Speaker: Jeff Rushall (NAU)

Abstract: This week’s talk deals with just a few of the historic figures in our discipline that met untimely and/or gross and/or tragic ends.

The faculty guest will be Gina Nabours. [PDF of Flyer]

### Ramanujan’s Impossible Sum

Date: Friday, September 17

Speaker: Jeff Rushall (NAU)

Abstract: The topic this week is the Ramanujan’s Impossible Sum, and deals with that funny-looking $1 + 2 + 3 + \cdots = -1/12$ formula. I’ll show why the formula seems to be true, why it seems to be nonsense, and do my best to make fun of mathematicians who believe it (like me), mathematicians who don’t believe it (like me), and physicists who may or may not believe it (including Dr. David Cole from the Department of Astronomy and Planetary Science here at NAU, who will be attending).

The faculty guest will be Matt Fahy.

### The Collatz Conjecture

Date: Friday, September 10

Speaker: Jeff Rushall (NAU)

Abstract: The topic this week is the Collatz Conjecture, a simple yet devilishly difficult unsolved problem in number theory. See the flyer linked below for more information.

The faculty guest will be Dana Ernst. [PDF of Flyer]