# Archived Math Circle Material

## Previous Talks Fall 2012

Date and RSVP links | Speaker | Topic (click for more info) | Event and poster links |
---|---|---|---|

October 1, 2012: Register | Richard Askey | Counting: to and then beyond the binomial theorem | Combined High School Math Night & Math Circle (Poster) |

October 8, 2012: Register | Philip Matchett Wood | Proofs with Parity | Math Circle |

October 15, 2012: Register | Philip Matchett Wood | Fun Flipping Coins | Math Circle (Poster) |

October 22, 2012: Register | Saverio Spagnolie | Random walks: how gamblers lose and microbes diffuse | Combined High School Math Night & Math Circle (Poster) |

October 29, 2012: Register | Beth Skubak | non-Euclidean geometry | Math Circle (Poster) |

November 5, 2012: Register | Mihai Stoiciu | Rubik's Cubes | Combined High School Math Night & Math Circle (Poster) |

November 12, 2012: Register | Alison Gordon | Curious Catalan Numbers | Math Circle (Poster) |

November 19, 2012: Register | Gregory Shinault | Tiling Problems | Math Circle |

November 26, 2012: Register | Claire Blackman | Binary Numbers | Math Circle |

### Counting: to and then beyond the binomial theorem

October 8th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Richard Askey.** How many ways can zeros and ones be put into n places?
It is easy to see this is 2^n. It is also easy to show that there
are n! ways of ordering n different objects. There are problems
which go beyond these two. How many ways can k zeros and n-k ones be
put into n places? How many inversions are there in the n! ways of
ordering the numbers 1,2,...,n. [123 has no inversions, 132 has one,
312 has two, 321 has three]. These will lead us to what has been
called "The world of q".

### Proofs with Parity

October 8th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Philip Matchett Wood.** Parity---matching objects up in pairs---is a surprisingly useful tool for answering math questions. Bring a pencil and notebook, and we will explore many different situations where parity plays a role.

### Fun Flipping Coins

October 15th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Philip Matchett Wood.** Flip a coin many times, and what happens? A whole mess of cool probability, that what! Bring a notebook, pencil, and some sharp common sense.

### Random walks: how gamblers lose and microbes diffuse

October 22nd, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Saverio Spagnolie.** We will explore one of the most famous mathematical models of random activity, the random walk. After an introduction to some basic ideas from probability, we will see that the same mathematical tools can be used to study completely different types of problems. In particular, we will find that there are no gambling strategies that can be used to beat the casino, and that tiny microorganisms can't stop moving even if they want to!

### Non-Euclidean geometry

October 29th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Beth Skubak.**
Most of the geometry we see in school is based on the ideas of the Greek mathematician Euclid, who lived around 300 BC. While his ideas are pretty useful, we want to consider geometry in some "non-Euclidean" scenarios, like when instead of being flat, our surfaces are curved.

### Rubik's Cubes

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

**Presenter: Mihai Stoiciu.** Rubik's Cubes. Some people describe mathematics as the science of patterns. We will explore patterns, permutations, orientations, and counting with the famous Rubik's Cube.

### Curious Catalan Numbers

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

**Presenter: Alison Gordon.** The Catalan numbers are a sequence that shows up as solutions to all sorts of problems in mathematics. Join us as we count handshakes, match parentheses, and build mountains in order to understand these interesting numbers!

### Tiling Problems

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

**Presenter: Greg Shinault.** Remember tangrams? You know, given some tiles build a specific shape using them. That is an example of a tiling problem, and to some mathematicians they are serious business. We are going to play with a variety of these puzzles, and talk about some of the things that have been figured out about them.

### Binary Numbers

November 26th, 2012, **6pm**, Van Vleck Hall room B223, UW-Madison campus

**Presenter: Claire Blackman.** We're all used to doing arithmetic with the 10 digits 0 to 9. But there's no reason why we shouldn't use just two digits, 0 and 1, instead. We'll be exploring the world of binary arithmetic, which is based on powers of two.

## Previous Talks Spring 2012

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.