# Archived Math Circle Material

## Contents

## Previous Talks

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

Date | Speaker | Talk (click for more info) |
---|---|---|

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

### Madison Math Circles

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.