# Madison Math Circle

## Contents

- 1 What is it?
- 2 Alright, I want to come!
- 3 Questions?
- 3.1 Infinitely Often
- 3.2 Making taffy with the Golden mean
- 3.3 Guarding an Art Gallery
- 3.4 The Coming of Enigma
- 3.5 Origami
- 3.6 The Game of Nim
- 3.7 Pythagorean Triples: A Personal Interview
- 3.8 Doodling and Graph Theory
- 3.9 A Mathematician's April Fools
- 3.10 String puzzles
- 3.11 How to Win (or not) at Tic-Tac-Toe
- 3.12 Playing with Zomes
- 3.13 TBA
- 3.14 Archived Math Circle Material

# 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 snacks 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!

Sign up for our email list: https://lists.math.wisc.edu/listinfo/math-circle

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 B231, on the UW-Madison campus).
**We'd also appreciate if you click the "Register" link for the date 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** (Lalit Jain, Betsy Stovall, and Philip Matchett Wood): math-circle-organizers@math.wisc.edu.

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### Infinitely Often

February 4th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

** Infinitely Often**

So you think you can add two numbers, three number, even a lot of numbers together? Well, can you add an infinite number of numbers together? See how thinking about infinite processes can be used to add infinite sums, evaluate repeating decimals, understand infinite continued fractions, and calculate areas and volumes. Also see what strange things can go wrong when dealing with infinity.

### Making taffy with the Golden mean

February 11th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

** Making taffy with the Golden mean**

Taffy pullers are devices used to make candy or bread. They are very interesting mathematically: we can relate the number of folds of dough to some famous mathematical sequences. Some surprising numbers pop up, like the Golden mean but also its lesser-known cousins. We can use this knowledge to improve existing devices. (Warning: no actual taffy will be made. Sorry.)

### Guarding an Art Gallery

February 18th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

**Guarding an Art Gallery**

How many guards does it take to guard an art gallery so that every spot in the gallery can be seen by at least one guard? We will explore this question and find an upper bound on the number of necessary guards based only on the number of walls in the gallery.

### The Coming of Enigma

Special Public Lecture: Wednesday, February 27th, 2013, **5pm**, Van Vleck Hall room **B239**, UW-Madison campus

The Enigma machine was a cryptodevice used by the Germans before and during World War II and was considered to provide unbreakable security. This belief was founded on very solid principles which will be outlined in this talk. Taking a two-millennia tour through the history of cryptology, we will come to understand the design principles that went into the Enigma and understand how it worked and how it was used. We will also touch on how espionage, treason, and sibling rivalry provided Polish mathematicians the necessary ingredients to break the unbreakable. This talk is geared towards the general public, with no specific expertise in mathematics assumed.

### Origami

February 25th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

Origami is the art of folding paper, and it involves some cool math, too. Come to find out more!

### The Game of Nim

March 4th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

Nim is a two-player game wherein the players alternate taking one or more stones from a pile (there are two or more piles at the beginning). The player who takes the last stone wins. We will spend most of the time playing and trying to come up with winning strategies. At the end, we will talk a little about the history a general strategy to win the game.

### Pythagorean Triples: A Personal Interview

March 11th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

We all know the Pythagorean theorem from geometry, which tells us the relationship between the side lengths of any right triangle: a^2 + b^2 = c^2, where c is the length of the hypotenuse. Sometimes we are very lucky, when a, b, and c are natural numbers such as 3, 4, and 5. That is called a Pythagorean triple. We're going take a close look at these characters and figure out a few of their less-than-obvious traits.

### Doodling and Graph Theory

March 18th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

Some of the pencil-and-paper games we play in notebook margins use more math than meets the eye. We'll try out a few fun and simple doodling puzzles, and see how they translate to some basic questions in graph theory. Then we'll harness our new theory to find quick solutions to whole groups of puzzles.

### A Mathematician's April Fools

April 1st, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

A paradox is a seemingly logically valid argument that leads to absurd conclusions. Mathematicians are always very careful to avoid accidentally using one, but they can be useful and fun to play with.

### String puzzles

April 8th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

They may be familiar from novelty shops or even your mantlepiece--a bit of string wound around and through some configuration of objects, asking you to accomplish some apparently impossible rearrangement or removal. Part of their difficulty comes from hopelessly infinite array of available moves--do you perhaps tie a clever knot here? Maybe pass a bight through there? We'll look at a few examples and see how to distill them to something more manageable, and even turn some into puzzles that can be solved instead only on paper (no drawing skills required).

### How to Win (or not) at Tic-Tac-Toe

April 15th, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

### Playing with Zomes

April 22nd, 2013, **6pm**, Van Vleck Hall room B231, UW-Madison campus

This week we will and study the symmetric and magic of 3 dimensional shapes. Be ready to get your hands dirty and make your own stellated icosahedron!

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### TBA

**To Be Announced:**
Keep an eye out---we'll have more information soon!