Monthly Math Hour Archive
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2024

Sunday, March 3 2024, 1:00–2:00 PM, at UW in ARC (Architecture building) , room 147.
Geometric miracles
Sergey Fomin , University of Michigan.Abstract: Pick a few points on the plane. Draw several lines through them. Mark some points on these lines, such as the points where the lines intersect. Draw additional lines through some of these points, and so on. Sometimes this process produces miracles: points lying on the same line for no obvious reason. I will explain where these miracles are coming from.
Worksheets from the talk: The following worksheets require Geogebra, which can be downloaded here , or accessed through a browser here . Click on the following to download the worksheets: first worksheet , second worksheet .

Sunday, April 21 2024, 1:00–2:00 PM, in ARC (Architecture building) , room 147.
Slicing Space
Cynthia Vinzant , University of Washington.Abstract: Suppose we lazily slice up a pizza. How many pieces can we make with just a few straight cuts? What if we don't like crusts? What if we had a watermelon? Together we will try to answer these questions and explore some of the beautiful geometry behind them.
Slides from the talk are here .

Sunday, May 19 2024, 1:00–2:00 PM, in ARC (Architecture building) , room 147.
Small Boundaries and Circular Reasoning
Stefan Steinerberger , University of Washington.Abstract: Many things in nature are approximately round: the earth, my head and an apple being obvious examples. One reason is that round things tend to have a relatively small surface area. This is a very old story that started 2700 years ago with the adventures of Queen Dido in the ancient kingdom of Carthage and took many, many centuries to be resolved. While at it, we are also going to take a really good look at what it really means to be a boundary or a surface. It's clear that a wall is usually the boundary of a room and we also have a good idea of what the surface of an apple would look like. We'll have a look at some crazier examples where it becomes harder to say what a boundary really is, the story keeps going!
Slides from the talk are here .
2023
Sunday, March 12 2023, 1:00–2:00 PM, at UW ARC 147
Strategic Game Theory
XiaoLin Danny Shi , University of Washington
Links: Recording , slides
Sunday, April 23 2023, 1:00–2:00 PM, at UW ARC 147
Visualizing Mathematics: Solving Problems Without Numbers
Kristine Hampton , University of Washington
Link: Recording
Sunday, May 21 2023, 1:00–2:00 PM, at UW ARC 147
Counting in Catalan: Handshakes, Trees, and Paths
Kyle Ormsby , Reed College and University of Washington
Abstract: In this talk, we'll uncover how trees, parentheses, handshakes, triangulations, and mountain ranges are all counted by the sequence of Catalan numbers: 1, 1, 2, 5, 14, 42, …. Along the way, we'll learn the fundamentals of combinatorics — the mathematics of counting — including the additive and multiplicative counting principles, factorials, binomial coefficients, recurrence, and the one concept that rules them all: bijection. We'll conclude by contemplating an open question that has stumped mathematicians for over 100 years — maybe you can solve it!
Links: Recording , slides
2022
Sunday, March 20, 1:00 PM
Patterns in permutations
Lara Pudwell , Valparaiso University
A permutation is a list of numbers where order matters. While it is wellknown that there are n! ways to put n different numbers in order, there are a variety of followup questions to explore, especially when we study permutations that have specific properties. In this talk, we will focus on permutation patterns – that is, smaller permutations contained inside of larger permutations. From a pure mathematics perspective, permutation patterns lead to a variety of interesting counting problems. Looking further afield, these patterns have connections to computer science, chemistry, and more!
Links: video , slides , further reading: link 1 , link 2
Sunday, April 10, 1:00 PM
Boards, cards, and coins
Dimitar Grantcharov , University of Texas, Arlington
We'll talk about games involving boards, cards and coins, and discuss winning strategies and the invariants which can help you win!
Link: video
Sunday, May 22, 1:00 PM
Multiplication algorithms, new and old
Ricky Liu , University of Washington
What's the fastest way to multiply? We'll take a look at multiplication tools and methods from antiquity to present day and discover whether there is a faster way to multiply than what you were taught in school.
2021
Sunday, March 21, 1:00 PM
Nora Youngs , Colby College
Neurons, navigation, and convexity
Links: video , slides
Sunday, April 25, 1:00 PM
Dylan Wilson , Harvard University
Numbers and shapes
Links: video , slides
Here is the link for visualizing the quaternions that Dylan mentioned at the end of his talk: click here
Sunday, May 23, 1:00 PM
Dimitri Zvonkine , Laboratoire Mathématiques de Versailles
Hinge mechanisms
Click here for links used in the talk
Sunday, June 13, 1:00 PM
Carolina Benedetti , Universidad de los Andes
The game of set: clocks with 3 hours
2020
April 12, 2020, 1:00 PM
Jonah Ostroff , University of Washington Department of Mathematics
How to be extremely good at dots and boxes
Dots and Boxes is a pencilandpaper game that you may have played before: draw a square array of dots, take turns drawing lines between them, and try to complete more boxes than your opponent. The rules are quite simple, but the math is remarkably complicated! We'll learn a few layers of strategy you can use to astound and humiliate your friends, and then discuss how variations in the rules can affect this strategy.
Video of the talk
April 26, 2020, 1:00 PM
Kristin DeVleming , University of California, San Diego Department of Mathematics
Rotations, reflections, and rearrangements
Symmetries and rigid motions are everyday examples appearing in the beautiful subject of group theory, which we'll approach in a handson way. Get ready to move some objects (and yourselves!) around while learning about groups as we dive into abstract algebra.
Video and slides for the talk
May 17, 2020, 1:00 PM
Tom Edgar , Pacific Lutheran University Department of Mathematics
You're my better half: a tale of complimentary complementary sequences
We investigate a special class of sequences called Beatty sequences. These sequences come in pairs, and we'll demonstrate and prove a result known as Rayleigh's theorem, which says these pairs always break the counting numbers into two disjoint groups. We'll then investigate a more general process for formulaically constructing pairs of complementary sequences. If time permits, we may also discuss a few applications of Beatty sequences.
Video and slides for the talk
June 7, 2020, 1:00 PM
Cliff Mass , University of Washington Department of Atmospheric Sciences
The mathematics of weather prediction
All weather forecasts are dependent on numerical weather prediction in which large supercomputers are used to solve the equations describing the physics of the atmosphere. This talk will describe the history of numerical weather prediction and how the solution of a complex collection of equations allows simulation of the future state of the atmosphere.
Video and slides for the talk
2019
May 19, 2019
Bianca Viray, University of Washington, Mathematics
The game of SET:
finding patterns in
differences
SET is a card game where the goal is to find collections of three cards where each of features (color, shape, number, and shading) are all the same or all different. This simple game surprisingly leads to lots of interesting mathematics, including a question which remains unsolved!
Flyer
Video of the talk
Slides from the talk
April 28, 2019
Natasha Rozhkovskaya, Kansas State University, Mathematics
Math questions from
an art museum
We will look at three works of art by Sol Lewitt, Maurits Cornelis Escher and Carlo Crivelli and use them to explore mathematical questions in the fields of combinatorics, complex analysis, and Euclidean geometry.
Flyer
Summary of the talk
March 17, 2019
Sara Billey & Timea Tihanyi, University of Washington, Mathematics & School of Art + Art History + Design
Tactile patterns in art
and math
Video of the talk
2018
May 20, 2018
David Pengelley, Oregon State University
All Tangled Up and Searching for the Beauty of Symmetry?
Flyer
Video of the talk
April 15, 2018
Jennifer McLoudMann, UW Bothell
One Tile at a Time: Mathematicians' Quest to Discover All Convex Polygonal Tessellations
Flyer
Video of the talk
March 25, 2018
Henry Cohn, Microsoft Research
Dense Sphere Packing In a Million Dimensions
Flyer
Video of the talk
Slides from the talk
2017
May 7, 2017
Savery 260
Paul Zeitz, University of San Francisco, Mathematics
The game is rigged!
Flyer
Slides
Video Recording (
Exercises
We will look at a variety of wagers and games that guarantee a nearly perfect probability of success to the player who makes the best mathematical analysis. It's not all fun and games, though: our vignettes have important mathematical morals. See the Exercises link for an explanation of the puppies and kittens game strategy.
April 9, 2017
Savery 260
Mohamed Omar, Harvey Mudd College, Mathematics
Areas of polygons and counting
Flyer
Finding the area of a general polygon can be quite complicated, especially when it has many sides and strange angles at its vertices. However, for a special class of polygons, there is a beautiful formula for determining their areas that has amounts to counting dots on a page! This talk will guide us through the development of the special formula.
March 12, 2017
Savery 260
Emily M. Bender, University of Washington, Linguistics
The mathematics of language
Flyer
Slides
Video Recording (
Mathematics can be used to model how language works and to measure the similarities and differences between different languages. From this, we can build computer software that will automatically process speech and text, for applications such as machine translation, voice activated computer interfaces, and autocorrect. In this talk, we will explore how mathematical objects called trees and feature structures, together with an operation called unification can be used to model English sentences (and also pizza preferences!). We will also learn about how computers are better at finding ambiguity in natural language than people are, but worse at resolving it.
2016
May 15, 2016
Gowen 301
Anna Karlin, University of Washington, Computer Science
Stable Matching
Flyer PDF
Video Recording (
In 2012, a Nobel Prize in Economics was given in part for the solution to the following problem: Say we have 100 boys and 100 girls and we want to make them into couples. Everyone makes a list of their ideal partners from 1 to 100 in order of most favorite to least favorite. The question now is whether there is a way to match everyone up so that the matching is “stable”: This means that there is no couple (A,B) in our matching where girl A prefers some other boy to B and boy B prefers some other girl to A. In this Math Hour, you will learn about an efficient algorithm for solving this problem and the fascinating properties of stable matchings.
April 17, 2016
Savery 260
Dominic Klyve, Central Washington University, Mathematics
The Life, Legacy, and the Lost Library Books of Leonhard Euler
Flyer PDF
April 15 is the birthday of Leonhard Euler – one of the greatest and most prolific mathematicians in history. This talk will examine the life of Euler, and will discuss some of his major accomplishments, in fields ranging from number theory to geometry. We will also tell stories of the speaker's role in creating the online “Euler Archive” and of the fascinating old books by Euler he discovered in several libraries.
March 20, 2016
Savery 260
Jayadev Athreya, University of Washington, Mathematics
Bouncing balls, fractions, and grids
Flyer PDF
Video Recording (
We will discuss how studying the path of a ball bouncing around a square room connects to the study of fractions and the study of grid patterns. The talk will be elementary and showcase connections between geometry, algebra, and number theory. Lots of pictures and patterns!
2015
May 17, 2015
Edwin O'Shea, James Madison University
Euclid's Elements: An old and beautiful math book and its influence on Lincoln (flyer ) – video (
Euclid's Elements from Ancient Greece is to mathematics what Shakespeare is to literature, being initially difficult to read but providing the first substantial example of the tremendous possibilities in mathematics. Among the many great results in Elements are Pythagoras's Theorem and the fact that a mysterious constant called π actually exists. We will spend much of this talk showing how these well known results from geometry came to be, emphasizing both mathematical intuition and mathematical proof. We will close with why this old math book was so deeply influential on Jefferson's Declaration of Independence and on Lincoln's understanding of the wrongs of slavery.
April 12, 2015
Jonah Ostroff, University of Washington
Mildly Impressive Mathematical Card Tricks (flyer ) – slides , video (
In this talk, we'll look at a bunch of twoperson magic tricks, centered on a common theme: how can you convey a lot of information with a small number of choices? We'll see a few examples of these tricks, and then learn a famous theorem that tells us why they work and when they don't. No slight of hand required, but you might need to do some arithmetic.
March 22, 2015
Brandy Wiegers, Central Washington University
Mathematical Tiling and Organization (flyer ) – handout , slides , video (
There are many mathematical problems that involve tiling (covering) all the squares on a chessboard (or similar board) with tiles of various sizes. We'll be talking about these problems and then taking tiling to the next level, with new shapes and sizes of tiles covering all types of surfaces. Plan to roll up your sleeves and move those tiles around.
2014
May 18, 2014
Vic Reiner , Department of Mathematics, University of Minnesota, Guarding an Art Gallery (flyer ) – video available here
Slides
How many museum guards do you need to post to see every bit of wallspace in a weird art gallery having N straight walls that meet at funny angles? We'll see why you need N/3 guards at most and how this relates to cutting polygons into triangles.
April 27, 2014
Allison Henrich , Department of Mathematics, Seattle University, A Mathematical Tale of Games on Knots
(flyer ) – video available here
Slides , worksheet , papers: A Midsummer Knot’s Dream , The Link Smoothing Game
When you imagine what a mathematician does all day, you probably picture someone standing at a chalkboard covered in equations and numbers. It�s true that many of us do fulfill this stereotype at times, but we also draw amazing and beautiful pictures and think about things that may not seem obviously to be mathematical. In fact, there are many mathematicians who devote their time to thinking about knots. (Think: tying a knot in your shoelace or trying to untangle your headphones.) Some of us even do research on games! We invent interesting games then try to figure out what strategies players can use to win. In my talk, I will show how these two areas of research may actually be combined into an incredibly fun kind of mathematics. We�ll play several games using knots and links and discuss ways we can �stack the deck� and guarantee ourselves a win.
March 16, 2014
Jack Lee , Department of Mathematics, University of Washington, The Curvature of Space
(flyer ) – video available here
Do you think that everything there is to know about geometry was already discovered ages ago? Think again. Since the time of Euclid, the history of geometry has been a dramatic saga that your middle school teachers probably won't tell you about. It led, more than a century ago, to the mindbending mathematical discovery that the threedimensional space we live in might be "curved," in much the same way as the twodimensional surface of the earth is curved.
In this talk you'll have a chance to learn what it could possibly mean mathematically for space to be curved, how we can detect it, and the fascinating story of how we got from Euclid to here. Along the way, you'll find out about "proofs" by professional mathematicians that turned out to be wrong, bitter personal battles over who was right and who was wrong, a milliondollar prize for solving a mathematical problem, and a mysterious modernday Russian mathematician who earned it but doesn't want it.
2013
May 5, 2013
Martin Tompa , University of Washington, Computer Science
Title: How to Win Some Games You’ve Never Heard Of –
Here are some games you may like to play with: Hackenbush , Toads and Frogs , Nim
Come and learn some games that you can teach your friends and then win! We will talk about some littleknown games for two players, including games called Hackenbush, ToadsandFrogs, and Nim. It is very easy to learn how to play these games: I will teach you all of them. But learning how to win these games is not nearly so easy. There is a lot of fascinating mathematics involved in the winning strategies.
April 14, 2013
Cliff Mass , University of Washington, Atmospheric Sciences
Title: The Mathematics of Weather Prediction –
Cliff Mass Weather Blog
Although most people identify weather prediction with presentations on their local news broadcast or weather web site, the technology behind prediction is highly complex and based on the numerical simulation of a series of partial differential equations. In this presentation I will discuss the history, technology, and mathematics behind weather prediction, and will describe the future transition to probabilistic forecasting.
March 10, 2013
Jonah Ostroff , Brandeis University, Mathematics
Title: The Problem of Apportionment –
Article I, Section 2 of the US Constitution states that the number of representatives assigned to each state should be proportional to its population, but what exactly does that mean? It turns out that our nation's founders weren't exactly sure. What resulted was 150 years of politicians, bureaucrats, and mathematicians arguing over a surprisingly tricky math problem. We'll attempt to answer this question ourselves, and then walk through the history that brought us to the method used today.
2012
May 13, 2012
Location: Room 260, Savery Hall
Speaker: Eric Brechner, Principal Development Manager, Xbox Engineering Fundamentals
Title:"Rainbow Mathematics"
Video available here
Slides available here
Abstract: What time of day is best to see a rainbow? Why is a rainbow shaped like an arch? Which color is on top? Are there ever two rainbows at once?
Rainbows are uncommonly beautiful. Most people have seen them, especially here in Seattle. Yet, most people don't know a rainbow's secrets. A little optics, some math, and your imagination are all you need to unlock rainbows and reveal things few people know. You'll uncover them all for yourself in this engaging talk that turns Snell's law, water, sunlight, and reflection into a beautiful sight.
April 15, 2012
Location: Room 260, Savery Hall
Speaker: Steven Klee from the UC Davis Department of Mathematics
Title: "The Mathemagic of Magic Squares"
Video available here 
Slides available here 
Abstract: A magic square is a filling of the squares of an n x n grid with the
numbers 1, 2, 3, ..., n^{2} so that the numbers in all rows and columns
have the same sum. In this talk, we will explore the history of magic
squares, from ancient mathematicians in China, India, and Persia, to
Benjamin Franklin's fascination with constructing magic squares and modern
mathematical problems. We will explore the underlying mathematics of magic
squares. We will end by taking the magic out of magic squares and using
them to understand a mathematical game.
March 11, 2012
Location: Room 260, Savery Hall
Speaker: Professor Jonathan Brundan from the University of Oregon Department of Mathematics
Title: "Domino Tilings and Determinants"
Video available here 
Handout available here 
Abstract:
There are two ways to tile a 2x2 board with 2x1 tiles (= or ).
There are thirty six ways to tile a 4x4 board with 2x1 tiles (you can
check this by listing all the possibilities!).
Question: How many ways are there to tile an 8x8 board with 2x1 tiles?
I'll explain a neat way to work this out using some techniques from graph theory and linear algebra  though no knowledge of that will be assumed in advance. If there's time I'll talk about some other related combinatorial/counting problems.
2011
May 15, 2011
Location: Room 260, Savery Hall
Speaker: Professor Sara Billey from the University of Washington Department of Mathematics
Title: "Computer proofs in Algebra, Combinatorics and Geometry"
Slides available here 
Video available here 
Abstract: Have you ever tried to prove a theorem using a computer?
If not, this talk might give you some ideas to help you get started. If so,
this talk will hopefully encourage you to think about the next
questions  what types of problems are amenable to computer proofs
and how should one publish a computer proof?
We will survey some famous and some not so famous theorems with computer assisted proofs but no known humanonly proof. For example, the 4color theorem and Kepler's conjecture are known to be true only because of computer assisted proofs. In addition, we will discuss some current research where the proof is not reduced to a finite check but instead depends on reaching a halting condition.
Some useful references:
April 17, 2011
Location: Room 264, Savery Hall
Speaker: Dr. Daniel Finkel, Mathematician, Math for Love
Title: "Billiard Balls and Laser Beams"
Video available here 
Abstract: Imagine standing in a room made entirely of mirrors, with a light bulb in a particular spot. The light is on. You would imagine that the room would be totally illuminated. And yet, you are in complete darkness. How is this possible?
Welcome to the geometry of reflection, where our thoughts turn to laser beams bouncing off mirrors, or billiard balls ricocheting off the sides of a pool table. In this talk, we'll explore the extraordinary reflective properties of geometric shapes like rectangles, triangles, circles, ellipses, parabolas, and hyperbolas. In fact, it's possible to understand many of these shapes almost entirely in terms of their reflective properties.
There are tremendous applications in the real world for reflective geometry, from satellite dishes to solar power, engineering to art to architecture. Reflective geometry is also a great source of purely mathematical questions, including a number of unsolved problems. We'll see the gamut in this lively talk on a unique topic.
March 13, 2011
Location: Room 260, Savery Hall
Speaker: Professor Sándor Kovács from the University of Washington Department of Mathematics
Title: "A glimpse into the sixth dimension"
Abstract: Higher dimensional geometry is used in more places than most people realize. Anyone who uses a mobile phone (is there anyone who does not?) takes advantage of higher dimensional geometry during every call. Higher dimensional geometry is used in robotics and cryptography. If you ever bought something on the internet, you were able to do that safely because of higher dimensional geometry.
The main purpose of this talk is to discuss higher dimensions from a practical angle. This is usually an intriguing topic if for nothing else but because it is so outofthisworld. My hope is that at the end of this discussion the idea of higher dimensions will seem perhaps less romantic and exotic, but more approachable and useful and definitely at least as intriguing as it had been before.
Many people have heard about time being considered the fourth dimension and perhaps even figured out ways to think about the fifth. In this talk we will go beyond both of that and as the main example of the usefulness of higher dimensions I will explain how the geometry of a six dimensional space can tell us about interesting questions regarding plane curves. The cell phone, robotics, and cryptography applications would require a semester long course at least, but I will say a few words about those as well and depending on time we will probably go up to working with 10 dimensions and say at least one word about the true dimension of the space we live in.
2010
June 6, 2010Speaker: Dr. Noble Hendrix, Biometrician, R2 Resource Consultants, Inc.
Title: "One Fish, Two Fish, False Fish, True Fish"
Abstract: Why do we count fish? The short answer isto eat them. A slightly longer winded explanation is, so that we can harvest fish at a rate such that the population can continue to replace itself. This scientific explanation makes several assumptions, though. Those assumptions are: we understand how fish populations increase and decrease naturally, we understand how fishing affects the population, and we know how accurate our counts of the population are.
I will talk about all three of these topics but mostly concentrate on the final one, because people (Homo sapiens) in general are not very good at counting. As an extreme example of this trait, members of the Pirahc tribe use a "onetwomany" system of counting, and lack a linguistic mechanism for numerals. Although we do not have the same linguistic constraints of the Pirahc, our counts of fish are inaccurate. To quantify the errors in counting, we can use probability models. For example, if I observed 10 fish what is the probability that there were actually 12?
There have been many technological improvements to counting fish. Each new approach has its own set of problems, though. Therefore, building probability models to understand the error in each successive technological breakthrough becomes a recurring process. We will look at some of the more interesting approaches to fish detection, such as video and acoustic imagery. The fundamental approach of using probability models to understand errors in measurement is, of course, not limited to counting fish. Probability models are applied in economics, medicine, and politics among other fields. Application in fisheries does have its unique benefits, however, and eating fish is certainly one of them.
May 16, 2010
Speaker: Professor Jennifer Quinn from the University of Washington at Tacoma Department of Mathematics
Title: "Fibonacci Fascination"
Abstract: Behold, the Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... , a number sequence which has long fascinated scholars because of its frequent occurrence in art, architecture, music, magic, and nature. You may have seen them in Dan Brown's novel The DaVinci Code or perhaps a FoxTrot cartoon. The next number of the sequence is generated by adding the two preceding. This talk will exhibit many natural examples of Fibonacci numbers while exploring the unusual (and aesthetically pleasing) patterns of the sequence itself. History and popular culture weave together with beautiful mathematics, plus a Fibonacci trick for good measure!
May 2, 2010
Speaker: Professor Jack Lee from the University of Washington Department of Mathematics
Title: "The Curvature of Space"
Abstract: Do you think that everything there is to know about geometry was already discovered ages ago? Think again. Since the time of Euclid, the history of geometry has been a dramatic saga that your middle school teachers probably won't tell you about. It led, more than a century ago, to the mindbending mathematical discovery that the threedimensional space we live in might be "curved," in much the same way as the twodimensional surface of the earth is curved.
In this talk you'll have a chance to learn what it could possibly mean mathematically for space to be curved, how we can detect it, and the fascinating story of how we got from Euclid to here. Along the way, you'll find out about "proofs" by professional mathematicians that turned out to be wrong, bitter personal battles over who was right and who was wrong, a milliondollar prize for solving a mathematical problem, and a mysterious modernday Russian mathematician who earned it but isn't sure he wants it.
 Click here to read more about the Poincare Conjecture from the Clay Mathematics Institute. Here, you can read about all seven Million Dollar problems posed by the Clay Institute.
 Here is another article from the Clay Mathematics Institute about Grigory Perelman's proof of the Poincare Conjecture.
 Here is an article from the New York Times discussing Perelman's original proof of the Poincare Conjecture in 2006.
 Here is another New York Times article from March 2010 discussing Perelman's rejection of the Clay Institute's $1,000,000 dollar prize!