1.6.7 How many pentagons and hexagons does it take to make a soccer ball?
All talks are at 6pm in Ingraham Hall room 120, unless otherwise noted.
September 22, 2014 DJ Bruce Is any knot the unknot?
October 6, 2014 David Sondak Fluids, Math, and Oobleck!
October 20, 2014 Scott Hottovy Coming soon!
January 26, 2015 TBA Coming soon!
February 9, 2015 Jeff Linderoth Coming soon!
February 23, 2015 Uri Andrews Coming soon!
March 2, 2015 Jordan Ellenberg Coming soon!
April 13, 2015 Jessica Lin Coming soon!
April 20, 2015 DJ Bruce Coming soon!
April 27, 2015 David Anderson Let's make a deal!
May 4, 2015 Daniel Ross Coming soon!
May 11, 2015 Grace Deane Last meeting of semester!
When does a simple picture solve a tricky puzzle? Come and learn about how line-and-dot drawing can solve complex puzzles, and create some new puzzles besides!
Is any knot the unknot?
Abstract: You're walking home from school, and you pull out your head phones to listen to some tunes. However, inevitably they are a horribly tangled mess, but are they really a knot? We'll talk about what exactly is a knot, and how we can tell when something is not the unknot.
We will explore the magical world of fluids and their relationship to mathematics. As an example of fluids and math in the real world, we will make the living fluid oobleck and discuss some of its mathematical properties.
We will discuss mathematical proofs that can be done using only pictures or figures. If you want to see many such examples you can check out the book "Proofs without Words: Exercises in Visual Thinking" by Roger B. Nelsen. For more information also look at the wikipedia page http://en.wikipedia.org/wiki/Proof_without_words , where you can find links to Java Applets that show animations of proofs without words, such as http://usamts.org/Gallery/G_Gallery.php .
We'll explore systems of arithmetic where numbers loop back around to zero (like the hours on a clock!), called "modular arithmetic". Which numbers are perfect squares in such systems? Gauss, one of the greatest mathematicians in history, called the remarkable answer the "golden theorem".
Infinity has a long history of having confounded and fascinated thinkers. We will take a look at some fundamental problems that early mathematicians grappled with and see some ways to understand infinity that have contributed to how we do math today.
Infectious diseases in our communities often make it into daily conversation: "There's a nasty cold going around.", "It's the flu season, get your shots.", and even, "There are news of a zombie outbreak!" Come hear how math gets applied to something as messy as spread of disease. We will use our wits, pencils, and computers to understand the progress of headaches, common cold, zombie outbreaks, and even ebola, a disease that is currently making the news.
How do we get such clear photos of the comet in the news? A 20 watt transmitter sends signals 500 million km through space to us and yet amazingly they survive this ordeal error-free. What's behind this is error-correcting codes. I'll give some of the basics, some related puzzles, and some challenges.
A Palindrome is a word or a number that reads the same forward and backwards. For example, Hannah, radar and civic are palindromic words, and 34743, 6446 are palindromic numbers. We will explore some curious properties of palindromes, and talk about what makes the number 196 special.
An ant is walking on a grid in the plane, but it can only move north or east. How many ways are there for it to get from one square to another? The numbers that appear when we answer this question have a wealth of interesting properties.
We will discuss simple ways to determine whether one number is evenly divisible by a smaller one and also how to prove these facts. If time permits, we will also look at divisibility rules in bases other than 10.
We will learn about motion subject to constraints. Mathematics based on these principles helps us build robots, explains human motion, and helps us model the shape of proteins like enzymes and antibodies.
We will explore a famous problem, called the Monty Hall Problem, that was inspired by a game show and became well known after a number of mathematicians incorrectly solved the problem in a very public manner. We will discuss and solve the problem, learn some probability, play the game, and invent some variants of the game that may, or may not, have similar counter-intuitive behaviors.
Abstract: We will learn some neat geometric tricks for quickly and painlessly computing some surprisingly large sums.
Abstract: Let's talk about the sine and cosine functions. One does not need to use very much information about these commonly seen functions in order to understand a large number of curves which can be drawn by graphing sine and cosine in Cartesian and polar coordinates. We will see sine curves, sums of sine curves, Lissajous figures, cycloids, hypocycloids, epicyclodes, and, of course, many rows of roses.
More details about each talk to follow soon. All talks are at 6pm in Van Vleck Hall, room B231, unless otherwise noted.
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.
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 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 is the art of folding paper, and it involves some cool math, too. Come to find out more!
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.
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.
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 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.
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).
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!
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".
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.
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.
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!
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.
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.
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!
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.
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.
March 26, 2012 Laurentiu Maxim How many pentagons and hexagons does it take to make a soccer ball?
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.
"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..."
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!
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.
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.
How many pentagons and hexagons does it take to make a soccer ball?
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 page was last modified on 28 August 2015, at 12:59.