# Madison Math Circle

## Contents

# What is it?

The UW-Madison math department organizes a series of talks aimed at interested middle school and high school students throughout the semester. Our goal is to present fun talks that give students a taste of interesting ideas in math and science. In the past we've had talks about plasma and weather in outer space, the way images are shaded in video games, and how credit card numbers are securely transmitted over the internet.

For more information about Math Circles see http://www.mathcircles.org/

After each talk we'll have **pizza** provided by the Mathematics Department, and students will have an opportunity to mingle and chat with the speaker and with other participants, to ask questions about some of the topics that have been discussed, and also about college, careers in science, etc.

**The Madison Math circle was recently featured in Wisconsin State Journal:** http://host.madison.com/wsj/news/local/education/local_schools/school-spotlight-madison-math-circle-gives-young-students-a-taste/article_77f5c042-0b3d-11e1-ba5f-001cc4c03286.html

# Alright, I want to come!

Great! If you are a student, we hope you will tell other interested students about these talks, and speak with your parents or with your teacher about organizing a car pool to the UW campus (and tell us how many people are coming so we can purchase the appropriate amount of pizza!)

If you are a parent or a teacher, we hope you'll tell your students about these talks and organize a car pool to the UW (all talks take place in Van Vleck Hall room B223, on the UW-Madison campus). **We'd also appreciate if you email us the dates that your group will be attending**.

**Parking** on campus is free at most (but not all) outdoor parking lots after 4:30pm. Parking lots #25 (Elizabeth Waters) and #26 (Observatory Hill) may be the most convenient. These parking lots are on Observatory Drive just west of the intersection with Charter Street. If you park there, then walk east along Observatory Drive to the top of Bascom Hill, then turn right to Van Vleck Hall. See also the map at http://www.map.wisc.edu/?keyword=public%20parking

# Questions?

If you have any questions, suggestions for topics, or so on, just email the **organizers** (Ed Dewey, David Dynerman, Nathan Clement, Lalit Jain, Kevin Zamzow, and Gheorghe Craciun): math-circle@math.wisc.edu.

## Talks this semester

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

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 |

April 2, 2012 | Laurentiu Maxim | TBA |

### 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 12th, 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

** A note about how to behave at the Math Circle: As the number of students who attend the Math Circle has increased, we still hope that all students have a chance to ask questions or make comments. This becomes impossible if one or two students keep interrupting with an overwhelming number of comments. Therefore, we ask each student to limit the number of questions or comments to about 10. **