# Archived Math Circle Material

## Previous Talks

More details about each talk to follow soon. All talks are at 6pm in Van Vleck Hall, room B223, unless otherwise noted.

February 13, 2012 Patrick LaVictoire Transforms: Pictures in Disguise
February 20, 2012 Uri Andrews Hercules and the Hydra
February 27, 2012 Peter Orlik Madison Math Circles
March 5, 2012 Jean-Luc Thiffeault The hagfish: the slimiest fish in the sea
March 12, 2012 Cathi Shaughnessy Archimedes' method
March 19, 2012 Andrei Caldararu Games with the binary number system
March 26, 2012 Laurentiu Maxim How many pentagons and hexagons does it take to make a soccer ball?

### Transforms: Pictures in Disguise

February 13th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Patrick LaVictoire. How are computer graphics like a massive game of Sudoku? How does a CAT scan get a 3D picture from a bunch of 2D X-ray images? How can you make the same image look like different people when viewed from close up and far away? I'll discuss all these and more, with some neat illustrations and quick games.

### Hercules and the Hydra

February 20th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Uri Andrews. We will talk about important techniques of self-defense against an invading Hydra. The following, from Pausanias (Description of Greece, 2.37.4) describes the beginning of the battle of Hercules against the Lernaean hydra:

"As a second labour he ordered him to kill the Lernaean hydra. That creature, bred in the swamp of Lerna, used to go forth into the plain and ravage both the cattle and the country. Now the hydra had a huge body, with nine heads, eight mortal, but the middle one immortal. . . . By pelting it with fiery shafts he forced it to come out, and in the act of doing so he seized and held it fast. But the hydra wound itself about one of his feet and clung to him. Nor could he effect anything by smashing its heads with his club, for as fast as one head was smashed there grew up two..."

For more information on some of the conjectures discussed during this talk see http://en.wikipedia.org/wiki/Collatz_conjecture and http://mathworld.wolfram.com/CollatzProblem.html

February 27th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Peter Orlik. A short introduction to elementary and middle school activities in Madison like Mathematical Olympiad and Mathcounts will be followed by some challenging problems. Please bring your favorite pencils and be prepared to work!

### The hagfish: the slimiest fish in the sea

March 5th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Jean-Luc Thiffeault. The hagfish is a bottom-dwelling, scavenger fish that resembles an eel. It has some interesting peculiarities: first, it sometimes willingly ties itself in a knot. Second, it secretes a spectacular amount of slime, which is used in the cosmetics industry. For a long time the purpose of this slime was unknown, but recently scientists have filmed live hagfish using it. (I'll keep this purpose a secret until the talk...) I'll then discuss how we can apply mathematical tools to study hagfish slime.

### Archimedes' method

March 12th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Cathi Shaughnessy. Students will use Archimedes' classical method to determine bounds for the value of the number pi. Please BRING A CALCULATOR with you for this presentation. The presenter will provide compass, protractor, straightedge and worksheet for each student.

### Games with the binary number system

March 19th, 2012, 6pm, Van Vleck Hall room B223, UW-Madison campus

Presenter: Andrei Caldararu. I will present a few games and tricks which use the binary number system. For more information about binary numbers please see http://en.wikipedia.org/wiki/Binary_numeral_system

### How many pentagons and hexagons does it take to make a soccer ball?

March 26th, 2012, 6:30pm (note special time!!!), Van Vleck Hall room B223, UW-Madison campus

Presenter: Laurentiu Maxim. I will first introduce the concept of Euler characteristic of a polyhedral surface. As an application, I will show how one can find the number of pentagons on a soccer ball without actually counting them.

This was the last meeting this semester. We hope to see you again in September!