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(New page: =What is it?= The UW-Madison math department organizes a series of talks aimed at high school students throughout the semester. Our goal is to present fun talks that give students a taste ...)
 
 
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=What is it?=
[[Image:logo.png|right|600px]]
The UW-Madison math department organizes a series of talks aimed at 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.  


'''Important:''' After each talk we'll have '''pizza''' provided by the department, and students will have an opportunity to mingle and chat with the speaker to ask questions about college, careers in science, etc.
For the site in Spanish, visit [[Math Circle de Madison]]
=What is a Math Circle?=
The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department.  Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption.  In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion.  The talks are independent of one another, so new students are welcome at any point.


=Alright, I want to come!=
The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.
Great! If you're a high school 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 on the UW campus). '''We'd also appreciate if you [mailto:math-night@math.wisc.edu email] us the dates that your group will be attending''', so we can purchase the appropriate amount of pizza.


If you're a high school student, speak with your high school teacher about organizing a car pool to the math night (and tell us how many people are coming!)
[[Image: MathCircle_2.jpg|550px]] [[Image: MathCircle_4.jpg|550px]]


=Questions?=
If you have any questions, suggestions for topics, or so on, just email the Math Night organizers: [mailto:math-night@math.wisc.edu math-night@math.wisc.edu].


==Talks this semester==
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.
More details about each talk to follow. All talks are at 7pm in Van Vleck Hall B231.


'''The Madison Math Circle was 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 check it out]!
=All right, I want to come!=
Our in person talks will be at, <b>Monday at 6pm in 3255 Helen C White Library</b>, during the school year. New students are welcome at any point!  There is no fee and the talks are independent of one another. You can just show up any week, but we ask all participants to take a moment to register by following the link below:
[https://forms.gle/5QRTkHngWf43nmCC9 '''Math Circle Registration Form''']
All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the 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. 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 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).
== Fall Schedule ==
<center>
<center>


{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
{| style="color:black; font-size:120%" border="1" cellpadding="14" cellspacing="0"
|-
|-
! Date !! Speaker !! Talk (click for more info)
! colspan="4" style="background: #e8b2b2;" align="center" | Fall Schedule
|-
! Date !! Location and Room || Speaker || Title
|-
| Oct 7 || 3255 College Library || Caitlin Davis || How to Cut a Cake (Fairly)
|-
|-
| February 17th, 2011 '''still being held''' || Andrew Bridy || [[#Cryptography|Cryptography]]
| Oct 14 || 3255 College Library || Uri Andrews || Math, Philosophy, Psychology, and Artificial Intelligence
|-
|-
| March 10th, 2011 || Ed Dewey || [[#The 0.5th Dimension|The 0.5th Dimension]]
| Oct 21 || 3255 College Library || Sam Craig || Fractal geometry and the problem of measuring coastlines
|-
|-
| March 24th, 2011 || Lalit Jain || [[#Cutting & Pasting|Cutting & Pasting]]
| Oct 28 || 3255 College Library || Cancelled || Cancelled
|-
|-
| April 7th, 2011 || Balazs Strenner || [[#Tilings|Tilings]]
| Nov 4 || 3255 College Library || Sam Craig || Proofs of the Pythagorean theorem, new and old.
|-
| Nov 11 || 3255 College Library || Chenxi Wu || Heron’s method for approximating square roots
|-
| Nov 18 || 3255 College Library || Diego Rojas || Non-Transitive Dice: The Math That Doesn’t Play Fair
|-
| Nov 25 || 3255 College Library || Kaiyi Huang || A geometric investigation into a space shuttle failure
|-
| Dec 2 || 3255 College Library || TBA || TBA
|-
| Dec 9 || 3255 College Library || TBA || TBA
|-
| Dec 16 || 3255 College Library || TBA || TBA
|-
|-
| April 28th, 2011 || Prof. Nigel Boston || [[#Face Recognition|Face Recognition]]
|}
|}


</center>
</center>
----
===Cryptography===
<span style="background:#00FF00">February 17th, 2011</span> '''Update 2/16/11: still being held'''


'''The science of code making and code breaking'''
= Fall Abstracts =


Sending information securely over the internet is an enormous practical problem.  How can you be sure that no one is reading your email, or worse, stealing your credit card number when you buy something online?  Cryptography is the art of encoding a message so it looks like a string of random letters or numbers, and decoding it on the other side to get the original message back.  In this talk I'll show you some simple ways you can use math to encode and decode information, and how the same techniques can be used to attack codes and try to break them.  The branch of math used is called number theory, and the problems that come up are very simple to state and very hard to solve, leading right to current research that mathematicians are working on today.
=== Abstract 10/7 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Caitlin Davis'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: How to Cut a Cake (Fairly)'''
|-
| bgcolor="#BDBDBD"  | 
Imagine you and a friend are sharing a cupcake.  How can you cut the cupcake so that each of you gets your fair share?  If you've ever shared a cupcake (or some other treat) with a friend, you might have an answer!  Now what if you're sharing a cake with several friends?  Can we use the same strategy to cut the cake fairly? We'll talk about how math can be used to study questions like this.
|}                                                                       
</center>


====Speaker: [http://www.math.wisc.edu/~bridy Andrew Bridy]====
=== Abstract 10/14 ===
Andrew is a third year math Ph. D. student studying algebra and computer science. Before coming to graduate school, he taught high school math for a year and was deployed with the Peace Corps to Honduras. Andrew is an avid video game fan - you should ask him to tell you about his favorite PC video games of the late 1990's.
<center>
----
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
===The 0.5th Dimension===
|-
<span style="background:#00FF00">March 10th, 2011</span>
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Uri Andrews'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Math, Philosophy, Psychology, and Artificial Intelligence'''
|-
| bgcolor="#BDBDBD"  | 
People come to understand the truth via a process of arguing. This could be a philosophical debate. This could be an internal dialogue. This could be in a courtroom. This could be deciding with your family where to go for dinner. These are all different forms of argumentation, with different rules for when you are convinced. In a courtroom, you have to be convinced beyond a reasonable doubt, whereas when deciding where to go for dinner, you might just have to look hungriest to win. These processes can be mathematically modeled. Moreover, this is important for the modern goal of teaching a computer how to think and how to understand human reasoning (Artificial Intelligence).  
|}                                                                       
</center>


'''A Harrowing Journey to the 0.5th Dimension'''


We frequently think about two dimensional spaces, like a map of a country, or three dimensional spaces, like the Holodeck from Star Trek. But what exactly is "dimension", anyway? This turns out to be a surprisingly deep question, without a unique answer. But asking it is still useful, and leads us to the strange and beautiful notion of Hassdorf dimension, one of the fndamentals of fractal geometry, which gives a meaning to non-integer dimensions. We will discuss Haussdorf dimension and its motivation, and see an application to psychology.  
=== Abstract 10/21 ===
<center>
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
| bgcolor="#BDBDBD"  align="center" | '''Title: Fractal geometry and the problem of measuring coastlines'''
|-
| bgcolor="#BDBDBD"  | 
A fractal is a shape which looks about the same when you look closely as when you look far away. I will show some examples of fractals that arise in math (like the Sierpinski triangle) and in nature (like the coastline of an island) and discuss the difficulties in determining what the length of a fractal means.
|}                                                                       
</center>


====Speaker: [http://www.math.wisc.edu/~dewey Ed Dewey]====
=== Abstract 11/4 ===
Ed is a first year Ph. D. student in mathematics. He used to be in a ska band.
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Sam Craig'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title: Proofs of the Pythagorean theorem, new and old.'''
|-
| bgcolor="#BDBDBD" |
The Pythagorean theorem has been known for thousands of years and over that time, people have found a number of different ways to prove the theorem. We will talk about a proof given by Pythagoras, a proof by US President Andrew Garfield, and a very recent proof (that you might have heard of in the news) by Calcea Johnson and Ne'Kiya Jackson.
|}
</center>
 
=== Abstract 11/11 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Chenxi Wu'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title:Heron’s method for approximating square roots.'''
|-
| bgcolor="#BDBDBD" |
We will talk about Heron's method for approximating square roots. This will lead us on a journey through approximation methods including Newton's method, through algebraic concepts like the p-adic numbers, and Hensel's Lemma.
|}
</center>
 
=== Abstract 11/18 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Diego Rojas'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title:Non-Transitive Dice: The Math That Doesn’t Play Fair.'''
|-
| bgcolor="#BDBDBD" |
What if I told you there’s a set of dice where winning doesn’t follow the rules you expect? In this talk, we’ll explore the strange and surprising world of non-transitive dice, where the usual logic of “if A is better than B, and B is better than C, then A must be better than C” simply falls apart. Using math, probability, and a little imagination, we’ll uncover why these dice defy intuition and how they challenge our understanding of competition and strategy. Get ready to think about games—and math—in a whole new way!
|}
</center>
 
 
=== Abstract 11/25 ===
<center>
{| style="color:black; font-size:100%" border="2" cellpadding="10" width="700" cellspacing="20" table
|-
| bgcolor="#e8b2b2" align="center" style="font-size:125%" | '''Kaiyi Huang'''
|-
| bgcolor="#BDBDBD" align="center" | '''Title:A geometric investigation into a space shuttle failure'''
|-
| bgcolor="#BDBDBD" |
We know that a circle has the same width in every direction, but is it the only object that has this property? NASA engineers assumed so, which, together with a string of other mistakes, might have led to the tragic failure of their space shuttle launch. Let’s look further into this problem so that we won’t make the same mistake again!
|}
</center>
 
==Directions and parking==
 
Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.
 
<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">
[[File: Helencwhitemap.png|400px]]</div>
 
'''Parking.''' Parking on campus is rather limited.  Here is as list of some options:
 
*There is a parking garage in the basement of Helen C. White, with an hourly rate.  Enter from Park Street.
*A 0.5 mile walk to Helen C. White Hall via [http://goo.gl/cxTzJY these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/Gkx1C in Lot 26 along Observatory Drive].
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], many spots ('''free starting 4:30pm''') [http://goo.gl/maps/vs17X in Lot 34]. 
*A 0.3 mile walk to Helen C. White Hall via [http://goo.gl/yMJIRd these directions], 2 metered spots (25 minute max) [http://goo.gl/maps/ukTcu in front of Lathrop Hall].
*A 0.2 mile walk to Helen C. White Hall via [http://goo.gl/b8pdk2 these directions] 6 metered spots (25 minute max) around [http://goo.gl/maps/6EAnc the loop in front of Chadbourne Hall] .
*For more information, see the [http://transportation.wisc.edu/parking/parking.aspx UW-Madison Parking Info website].
 
==Email list==
The best way to keep up to date with the what is going is by signing up for our email list. Please add your email in the form:
[https://docs.google.com/forms/d/e/1FAIpQLSe_cKMfdjMQlmJc9uZg5bZ-sjKZ2q5SV9wLb1gSddrvB1Tk1A/viewform '''Join Email List''']
 
==Contact the organizers==
The Madison Math Circle is organized by a group of professors and graduate students from the [http://www.math.wisc.edu Department of Mathematics] at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the '''organizers''' [mailto:mathcircleorganizers@g-groups.wisc.edu here]. We are always interested in feedback!
<center>
<gallery widths="500" heights="300" mode="packed">
File:Uri.jpg|[https://www.math.wisc.edu/~andrews/ Prof. Uri Andrews]
</gallery>
 
<gallery widths="500" heights="250" mode="packed">
</gallery>
</center>


----
==Donations==
===Cutting & Pasting===
Please consider donating to the Madison Math Circle. Our main costs consist of pizza and occasional supplies for the speakers.  So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from private donors. The easiest way to donate is to go to the link:
<span style="background:#00FF00">March 24th, 2011</span>


[http://www.math.wisc.edu/donate Online Donation Link]


The Bolyai-Gerwein theorem says that any two polygons of the same area have an "equi-dissection". In other words, there is a way to cut up one of the polygons into pieces (using straight line cuts) that can be rearranged to form the other. This deep theorem is surprisingly recent compared to much of classical geometry and has many interesting generalizations. During this weeks talk we will prove the theorem as a group using little more then argument by "scissors and glue."
There are instructions on that page for donating to the Math Department. <b> Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"!</b>  The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.


Here are some fun applets to see this in action:
Alternately, you can bring a check to one of the Math Circle Meetings.  If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check. 


http://demonstrations.wolfram.com/AnExampleOfTheBolyaiGerwienTheorem/
Or you can make donations in cash, and we'll give you a receipt.


http://www.cut-the-knot.org/Curriculum/Geometry/TwoRectangles.shtml
==Help us grow!==
If you like Math Circle, please help us continue to grow!  Students, parents, and teachers can help by:
* Like our [https://facebook.com/madisonmathcircle '''Facebook Page'''] and share our events with others!
* Posting our [https://www.math.wisc.edu/wiki/images/Math_Circle_Flyer_2021.pdf '''flyer'''] at schools or anywhere that might have interested students.
* Discussing the Math Circle with students, parents, teachers, administrators, and others.
* Making an announcement about Math Circle at PTO meetings.
* Donating to Math Circle.
Contact the organizers if you have questions or your own ideas about how to help out.


=Useful Resources=


An example of dissecting a square into pieces that form a triangle of the same area.
[[Image:TriangleSquare.jpg|200px]]




====Speaker: [http://www.math.wisc.edu/~jain Lalit Jain]====
== Archived Abstracts ==
Lalit is a first year Ph. D. student in mathematics interested in number theory and computer science. Before coming to graduate school, Lalit was a high school math teacher with [http://en.wikipedia.org/wiki/Teach_for_america Teach For America] in San Francisco. You should ask Lalit about who shot Frances in the video game Left 4 Dead.
----


===Tilings===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2023-2024 2023 - 2024 Abstracts]
<span style="background:#00FF00">April 7th, 2011</span>


'''Tilings'''
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2022-2023 2022 - 2023 Abstracts]


Tilings in the mathematical sense mean non-overlapping, gap-free coverings of the plane by certain shapes. For instance, one can take (infinitely many) squares and place them on the infinite plane as they are on a chessboard, nicely fitting next to each other. This is maybe the simplest example. But if one takes regular pentagons, it is impossible to form a tiling using only them.
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2021-2022 2021 - 2022 Abstracts]


The first class of interesting tilings we will discuss are the Penrose tilings. These involve two different shapes, the "kite" and the "dart". Not only it is fun to play with them and to try to make different arrangements, but these tilings have really interesting mathematical properties. Just to mention one of these: the ratio of the number of kites and darts - which I'll make precise - in all the possible arrangements is always the same, and it is the golden ratio!
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2020-2021 2020 - 2021 Abstracts]


Tilings have an artistic nature as well. The Dutch graphic artist M. C. Escher is famous for his math-connected drawings, and in fact many of these are tilings with funny shapes, birds for example. Another series of masterpieces by him are the woodcuts Circle Limit I-IV which picture hyperbolic tilings of the disk using funny graphics again. We will talk about their mathematical background, and also about how to write a program that makes a hyperbolic tiling out of an arbitrary image file.
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2019-2020 2019 - 2020 Abstracts]


[[Image:LW434.jpg]]
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2016-2017 2016 - 2017 Math Circle Page]
[[Image:LW361A.jpg]]
[[Image:kite and dart.gif]]


[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2016-2017 2016 - 2017 Abstracts]


====Speaker: [http://www.math.wisc.edu/~strenner/balazs/Home.html Balazs Strenner]====
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_2015-2016 2015 - 2016 Math Circle Page]
Balazs is a first year PhD student originally from Hungary, land of [http://en.wikipedia.org/wiki/Paul_Erd%C5%91s many] [http://en.wikipedia.org/wiki/Leo_Szilard fantastic] [http://en.wikipedia.org/wiki/John_von_Neumann mathematicians and scientists]. Balazs is quite merciless as the Deputy Sheriff in the card game [http://en.wikipedia.org/wiki/Bang! Bang!]


----
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_de_Madison_2015-2016 2015 - 2016 Math Circle Page (Spanish)]


===Face Recognition===
[https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle_Abstracts_2015-2016 2015 - 2015 Abstracts]
<span style="background:#00FF00">April 28th, 2011</span>


'''Invariant-Based Face Recognition'''
[https://www.math.wisc.edu/wiki/index.php/Archived_Math_Circle_Material The way-back archives]


I shall describe the main difficulties with automated face recognition and how our team of mathematicians, engineers, and computer scientists overcame some of them by using mathematical invariants.  
==Link for presenters (in progress)==
[https://www.math.wisc.edu/wiki/index.php/Math_Circle_Presentations  Advice For Math Circle Presenters]


What are invariants? Invariants are features that do not change under 3D rotation and translation. An example is the curvatures at the tip of the nose. These curvatures do not change, regardless of what angle you look at the face from. The problem though in practice is that curvatures are very sensitive to small changes in the measurements used to compute them, so that simply rounding of the measurements can lead to very different, not invariant numbers.
[http://www.geometer.org/mathcircles/ Sample Talk Ideas/Problems from Tom Davis]


For this reason, invariants have been rejected in the past for recognizing faces because they were not robust to measurement error, and so we decided to come up with a new family of robust invariants. I shall report how our implementation of this won us 2nd place in the 3D section of the national Face Recognition Grand Challenge.
[https://www.mathcircles.org/activities Sample Talks from the National Association of Math Circles]


====Speaker: [http://www.math.wisc.edu/~boston Professor Nigel Boston]====
[https://epdf.pub/circle-in-a-box715623b97664e247f2118ddf7bec4bfa35437.html "Circle in a Box"]
Nigel Boston is a Professor in the Departments of Mathematics and Electrical & Computer Engineering at UW-Madison. Nigel works in many interesting areas, including applying research from algebra and number theory to real world problems in engineering.

Latest revision as of 15:58, 25 November 2024

Logo.png

For the site in Spanish, visit Math Circle de Madison

What is a Math Circle?

The Madison Math Circle is a weekly series of mathematically based activities aimed at interested middle school and high school students. It is an outreach program organized by the UW Math Department. Our goal is to provide a taste of exciting ideas in math and science. In the past we've had talks about plasma and weather in outer space, video game graphics, and encryption. In the sessions, students (and parents) are often asked to explore problems on their own, with the presenter facilitating a discussion. The talks are independent of one another, so new students are welcome at any point.

The level of the audience varies quite widely, including a mix of middle school and high school students, and the speakers generally address this by considering subjects that will be interesting for a wide range of students.


MathCircle 2.jpg MathCircle 4.jpg


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 featured in Wisconsin State Journal: check it out!

All right, I want to come!

Our in person talks will be at, Monday at 6pm in 3255 Helen C White Library, during the school year. New students are welcome at any point! There is no fee and the talks are independent of one another. You can just show up any week, but we ask all participants to take a moment to register by following the link below: 

Math Circle Registration Form

All of your information is kept private, and is only used by the Madison Math Circle organizer to help run the 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. 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 3255 Helen C White Library, on the UW-Madison campus, right next to the Memorial Union).


Fall Schedule

Fall Schedule
Date Location and Room Speaker Title
Oct 7 3255 College Library Caitlin Davis How to Cut a Cake (Fairly)
Oct 14 3255 College Library Uri Andrews Math, Philosophy, Psychology, and Artificial Intelligence
Oct 21 3255 College Library Sam Craig Fractal geometry and the problem of measuring coastlines
Oct 28 3255 College Library Cancelled Cancelled
Nov 4 3255 College Library Sam Craig Proofs of the Pythagorean theorem, new and old.
Nov 11 3255 College Library Chenxi Wu Heron’s method for approximating square roots
Nov 18 3255 College Library Diego Rojas Non-Transitive Dice: The Math That Doesn’t Play Fair
Nov 25 3255 College Library Kaiyi Huang A geometric investigation into a space shuttle failure
Dec 2 3255 College Library TBA TBA
Dec 9 3255 College Library TBA TBA
Dec 16 3255 College Library TBA TBA

Fall Abstracts

Abstract 10/7

Caitlin Davis
Title: How to Cut a Cake (Fairly)

Imagine you and a friend are sharing a cupcake. How can you cut the cupcake so that each of you gets your fair share? If you've ever shared a cupcake (or some other treat) with a friend, you might have an answer! Now what if you're sharing a cake with several friends? Can we use the same strategy to cut the cake fairly? We'll talk about how math can be used to study questions like this.

Abstract 10/14

Uri Andrews
Title: Math, Philosophy, Psychology, and Artificial Intelligence

People come to understand the truth via a process of arguing. This could be a philosophical debate. This could be an internal dialogue. This could be in a courtroom. This could be deciding with your family where to go for dinner. These are all different forms of argumentation, with different rules for when you are convinced. In a courtroom, you have to be convinced beyond a reasonable doubt, whereas when deciding where to go for dinner, you might just have to look hungriest to win. These processes can be mathematically modeled. Moreover, this is important for the modern goal of teaching a computer how to think and how to understand human reasoning (Artificial Intelligence).


Abstract 10/21

Sam Craig
Title: Fractal geometry and the problem of measuring coastlines

A fractal is a shape which looks about the same when you look closely as when you look far away. I will show some examples of fractals that arise in math (like the Sierpinski triangle) and in nature (like the coastline of an island) and discuss the difficulties in determining what the length of a fractal means.

Abstract 11/4

Sam Craig
Title: Proofs of the Pythagorean theorem, new and old.

The Pythagorean theorem has been known for thousands of years and over that time, people have found a number of different ways to prove the theorem. We will talk about a proof given by Pythagoras, a proof by US President Andrew Garfield, and a very recent proof (that you might have heard of in the news) by Calcea Johnson and Ne'Kiya Jackson.

Abstract 11/11

Chenxi Wu
Title:Heron’s method for approximating square roots.

We will talk about Heron's method for approximating square roots. This will lead us on a journey through approximation methods including Newton's method, through algebraic concepts like the p-adic numbers, and Hensel's Lemma.

Abstract 11/18

Diego Rojas
Title:Non-Transitive Dice: The Math That Doesn’t Play Fair.

What if I told you there’s a set of dice where winning doesn’t follow the rules you expect? In this talk, we’ll explore the strange and surprising world of non-transitive dice, where the usual logic of “if A is better than B, and B is better than C, then A must be better than C” simply falls apart. Using math, probability, and a little imagination, we’ll uncover why these dice defy intuition and how they challenge our understanding of competition and strategy. Get ready to think about games—and math—in a whole new way!


Abstract 11/25

Kaiyi Huang
Title:A geometric investigation into a space shuttle failure

We know that a circle has the same width in every direction, but is it the only object that has this property? NASA engineers assumed so, which, together with a string of other mistakes, might have led to the tragic failure of their space shuttle launch. Let’s look further into this problem so that we won’t make the same mistake again!

Directions and parking

Our meetings are held on the 3rd floor of Helen C. White Hall in room 3255.

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Parking. Parking on campus is rather limited. Here is as list of some options:

Email list

The best way to keep up to date with the what is going is by signing up for our email list. Please add your email in the form: Join Email List

Contact the organizers

The Madison Math Circle is organized by a group of professors and graduate students from the Department of Mathematics at the UW-Madison. If you have any questions, suggestions for topics, or so on, just email the organizers here. We are always interested in feedback!

Donations

Please consider donating to the Madison Math Circle. Our main costs consist of pizza and occasional supplies for the speakers. So far our costs have been covered by donations from the UW Mathematics Department as well as a generous gifts from private donors. The easiest way to donate is to go to the link:

Online Donation Link

There are instructions on that page for donating to the Math Department. Be sure and add a Gift Note saying that the donation is intended for the "Madison Math Circle"! The money goes into the Mathematics Department Annual Fund and is routed through the University of Wisconsin Foundation, which is convenient for record-keeping, etc.

Alternately, you can bring a check to one of the Math Circle Meetings. If you write a check, be sure to make it payable to the "WFAA" and add the note "Math Circle Donation" on the check.

Or you can make donations in cash, and we'll give you a receipt.

Help us grow!

If you like Math Circle, please help us continue to grow! Students, parents, and teachers can help by:

  • Like our Facebook Page and share our events with others!
  • Posting our flyer at schools or anywhere that might have interested students.
  • Discussing the Math Circle with students, parents, teachers, administrators, and others.
  • Making an announcement about Math Circle at PTO meetings.
  • Donating to Math Circle.

Contact the organizers if you have questions or your own ideas about how to help out.

Useful Resources

Archived Abstracts

2023 - 2024 Abstracts

2022 - 2023 Abstracts

2021 - 2022 Abstracts

2020 - 2021 Abstracts

2019 - 2020 Abstracts

2016 - 2017 Math Circle Page

2016 - 2017 Abstracts

2015 - 2016 Math Circle Page

2015 - 2016 Math Circle Page (Spanish)

2015 - 2015 Abstracts

The way-back archives

Link for presenters (in progress)

Advice For Math Circle Presenters

Sample Talk Ideas/Problems from Tom Davis

Sample Talks from the National Association of Math Circles

"Circle in a Box"

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