## Girls’ Angle Bulletin, Volume 9, Number 5

Volume 9, Number 5 kicks off with an interview with the ADVANCE Professor of Computing at Georgia Institute of Technology, Dana Randall. Prof. Randall is also the Director of the Algorithms and Randomness Center and an Adjunct Professor of Mathematics.

Next, comes the concluding half of Heidi Hurst’s article on how she used math to help find optimal locations for FEMA Disaster Recovery Centers.

Emily and Jasmine continue their exploration of nice triangles by commencing with an exploration of which triangles have 3 “nice” angles and 2 sides of integer length. This is the last major case in their investigation of “nice” triangles and involves the most advanced mathematics.

Anna manages to generalize the result she found in the last issue to the finite fields $F_p$, where $p$ is prime. This result was known to Carl Friedrich Gauss.

We conclude with this summer’s batch of Summer Fun problem sets! This summer, we have contributions from Matthew de Courcy-Ireland, Aaron Levy, Lauren McGough (who is also a Girls’ Angle Advisory Board member and the Girls’ Angle Treasurer), Long Nguyen, and Zachary Sethna. Matthew, Aaron, Lauren, and Zachary are all graduate students at Princeton University. Long is an undergraduate at MIT.

We hope you enjoy it!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscr

## Girls’ Angle Bulletin, Volume 9, Number 4

Volume 9, Number 4 begins with an interview with Oberlin’s Andrew and Pauline Delaney Professor of Mathematics Susan Jane Colley, although as has been our practice, we truncate the interview in the electronic version. For the full version, please subscribe!

After a meditation on Miquel’s theorem, find out how a frog fish, dragon, and mathematician end up in the same story with the concluding half of The Mountain Clock, a fictional math story about an ancient city that adopted a 32-hour day.

Anna manages to prove a theorem she has been leading up to ever since Prof. Judy Walker suggested some exercises involving polynomials over the finite field with 2 elements.

Image courtesy of Heidi Hurst

Next comes a neat application of mathematics to disaster recovery.  Harvard University undergraduate Heidi Hurst spent a summer using math to figure out how to find optimal locations for Disaster Recovery Centers.  She explains her work in a two-part Math In Your World series.

Emily and Jasmine continue their exploration of nice triangles and establish a direct link between integer-sided triangles with perimeter p and partitions of p – 3 into parts with sizes 2, 3, and 4.

We conclude by unraveling some secrets of a marvelous recurrence relation created by one of our 11-year-old members.

We hope you enjoy it!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!

## Girls’ Angle Bulletin, Volume 9, Number 3

Volume 9, Number 3 begins with the concluding half of an interview with French mathematician Alice Guionnet. Prof. Guionnet is a professor of mathematics at MIT and an expert on random matrices.

The cover features an illustration by Julia Zimmerman for a fictional math story entitled The Mountain Clock.  The Mountain Clock tells the story of an ancient King who decreed a 32-hour day.

Katherine Cliff, a graduate teaching fellow at the University of Colorado, Colorado Springs, contributes this issue’s Math In Your World.  She brings the rational world of mathematics to the computation of probabilities for the Powerball lottery. If you work through this installment, you’ll be able to compute lottery probabilities and the value of a lottery ticket from scratch.

Anna continues her investigation of irreducible polynomials over the finite field with 2 elements. In this installment, she formulates 2 conjectures, works out implications of them, and proves one of them. Anna’s entire investigation traces back to an exercise suggested by Prof. Judy Walker in her interview from Volume 8, Number 6. Can you prove the conjecture she doesn’t prove?

Emily and Jasmine continue their quest for “nice” triangles. This time, they explore integer-sided triangles with no conditions at all on their angles. They determine the number of such triangles that have 2 given side lengths and begin to study the question of how many integer-sided triangles there are of a given perimeter.

In this issue’s Learn By Doing, you can try your hand at coming up with counterexamples. There are few things that so decisively prove a conjecture wrong than coming up with a counterexample!

There’s a lot more inside and we hope you enjoy it!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!

## Math Collaborations

##### This is a guest post by Vincent Marino, a math teacher at the Pollard Middle School in Needham, MA. Girls’ Angle has run 4 Math Collaborations there for seventh and eighth graders. For more information on Math Collaborations, please visit our website.

Thank you so much to Ken for allowing me to contribute a guest blog!  I am a middle school math teacher at the Pollard Middle School in Needham. I have had the extreme pleasure of having Ken come to Pollard for the past four years to host a Math Collaboration. The events have been thoroughly amazing. From a teacher’s perspective, there is nothing I enjoy more than seeing students working tirelessly and collaboratively towards a common goal.  The puzzles and problems that Ken puts together are the perfect balance of stretching students’ thinking while also making them attainable, and his gentle manner of prodding students without guiding them is something that I try to emulate on a daily basis in my own classroom.  I cannot do justice to how exceptional these events are, so I asked two students who participated in the latest Collaboration to write their thoughts on the event. Here is what they wrote.

“Recently we participated in the math collaboration treasure hunt hosted by Girls’ Angle. This event was after school on an early release day, and beforehand it didn’t seem like the best way to spend our time out of school. We were surprised by the complexity of the puzzles and impressed at how fast we solved it. It was a change to not be given detailed instructions or told exactly what to do. Instead we had to figure out how to be organized and efficient, without relying on adults. At first everything was chaotic and nobody knew exactly what to do. But then we established a system with small groups working on each problem, and everybody helping those who needed it. This activity taught us to work together and help others to achieve a common goal. In the end, we were only able to solve the puzzle because every single person contributed in some way. We had to be independent, work together, use leadership skills, be organized and listen to everybody’s ideas in order to complete the treasure hunt and receive the prize. This collaboration was an amazing learning experience and built leadership and teamwork skills, but more importantly a fun way to spend an afternoon.”

## Girls’ Angle Bulletin, Volume 9, Number 2

Volume 9, Number 2 begins with the first half of an interview with French mathematician Alice Guionnet. Prof. Guionnet is a professor of mathematics at MIT and an expert on random matrices.

In addition to the interview, there are 2 more articles in this issue that pertain to probability and statistics. One is the concluding half of Prof. Elizabeth Meckes articles on the laws of probability.  This time, she pulls up the curtain on the central limit theorem. The other is this issue’s Math In Your World, which describes an activity led by Girls’ Angle Support Network visitor Jinger Zhao. Jinger is a financial modeler who works at TwoSigma, a hedge fund based in New York City. At the club, Jinger uses statistics to model the connection between wingspan and height.

Anna continues her investigation of irreducible polynomials over the finite field with 2 elements. In this installment, she works out the roots of all the irreducible polynomials of degrees 4 and 5. Anna’s entire investigation traces back to an exercise suggested by Prof. Judy Walker in her interview from Volume 8, Number 6. Do you think you can see where Anna might be headed? If you do, follow your thoughts and see where they lead. You’re invited to tell us about it; we’d love to hear from you. If you’re falling in love with polynomials over $F_2$, check out this proposal for a new PolyMath project and the comments that follow.

Multiplication and exponentials are fundamental concepts in mathematics. For anyone working on learning these concepts, we hope Addie Summer’s Thoughts on Multiplication and our Learn by Doing on exponentials will be of use. The cover, which was created using MATLAB by MathWorks, honors multiplication.

Emily and Jasmine continue their quest for “nice” triangles. This time, they explore integer-sided triangles that have a 120 degree angle and establish a beautiful bridge between these and integer-sided triangles with a 60 degree angle.

We conclude with some notes from the club. If you’re a girl, aged roughly 10-18 in the Greater Boston Area, you’re welcome to join. Our next session begins January 28, 2016.

We hope you enjoy the Bulletin!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!

## Girls’ Angle Bulletin, Volume 9, Number 1

Volume 9, Number 1 features material from two mathematicians: an extensive interview with Elizabeth Munch, Assistant Professor of Mathematics at the University of Albany and the first of a two-part article on the laws of probability by Elizabeth Meckes, Associate Professor of Mathematics at Case Western Reserve University.

Prof. Munch’s road to mathematics is interesting in that music plays a significant role in her life.  In addition to her mathematical degrees, she also holds a degree in Harp performance from the Eastman School of Music. Find out how her musical studies affected her discovery of mathematics. In her interview, she mentions Takens embeddings, and the cover features a kind of Takens embedding.  The embedding is actually a 4-dimensional Takens embedding consisting of two spatial dimensions and two that extend into the color space.

Statistics plays an important role in so many sciences. Research would grind to a halt without it. One of the most important results in statistics is the central limit theorem. Prof. Meckes has contributed an eloquent two-part article that explains the meaning of this theorem. In part 1, she explains the laws of probability.

In Math In Your World, Lightning Factorial uses statistics to improve at darts, following the lead of statisticians Ryan Tibshirani, Andrew Price, and Jonathan Taylor, who showed in their paper A Statistician Plays Darts, that depending on your dart throwing prowess, you might be better off not aiming for the bull’s-eye.  Skeptical? Read Lightning’s article!

In Anna’s Math Journal, Anna continues her investigation of irreducible polynomials over the finite field with 2 elements. This investigation traces back to suggested exercises made by Prof. Judy Walker in the previous issue. If you’re unfamiliar with finite fields but want to follow along with Anna on her journey, this issue’s Learn by Doing is just for you. In it, finite fields are introduced assuming very little by way of prerequisites.
Meanwhile, Emily and Jasmine continue their quest for “nice” triangles. This time, they apply a technique that is often used to find Pythagorean triples to find formulas that yield the sides of all primitive triangles that contain a 60 degree angle, such as the 5-7-8 and 16-19-21 triangles.

We conclude with some notes from the club! We’ve got a wonderful group of members this semester and if you’re a girl in grades 5-12 who lives near Cambridge, MA, you’re welcome to attend!

We hope you enjoy it!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!