## 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!

## Katherine and Serena Visit the Museum

(Added October 1, 2015: This raffle is now closed. Thank you to all who entered. Congratulations to Fran M. who won the general draw and Iris L. who won the member draw!)

Can you reconstruct Serena and Katherine’s path through the museum? Continue reading

## Girls’ Angle Bulletin, Volume 8, Number 6

The object on the cover of Volume 8, Number 6 is called the Chebyshev Lollipop. It is based directly on an idea of Michael Trott. The mathematical content differs slightly from his creation which can be seen at MathWorld.

Chebyshev polynomials (of the first kind) appear in this summer’s batch of Summer Fun problem sets and in a new Emily and Jasmine series which commences in this issue.

Does this make you go “Hmm…”?

In school, Jasmine happened by a geometry class where the teacher had the peculiar figure shown at right on the board. That figure turned out to be the launch point for an adventure in search of nice triangles.

This issue’s interview is with the Chair of the Department of Mathematics at the University of Nebraska-Lincoln, Professor Judy Walker. In her interview, Prof. Walker gives some pointers for how to learn mathematics well, saying “I absolutely must work through examples.”

In Anna’s Math Journal, Anna takes up Prof. Walker’s specific example suggestion and explores finite fields with 4 and 8 elements

In Part 5 of our series on the derivative, we explore the derivative of the exponential function.

We wrap up with detailed solutions to this summer’s batch of Summer Fun problem sets which include proofs of the arithmetic-geometric mean inequality, a derivation of the Taylor series of the arctangent function, and a proof of Lagrange’s theorem that, in finite groups, the order of any subgroup divides the order of the group.

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!

## Origami-inspired Proof of the Pythagorean Theorem

While working with math teachers Richard Chang and Randi Currier of the Buckingham Browne & Nichols Middle School to come up with problems that use polynomials and rational expressions, we stumbled upon an origami-inspired proof of the Pythagorean theorem that I’d like to share. Continue reading

## Girls’ Angle Bulletin, Volume 8, Number 5

Volume 8, Number 5 of the Bulletin kicks off with an interview of Ivana Alexandrova. Ivana is an Assistant Professor of Mathematics at the State University of New York, Albany.  Among other things, she maintains a webpage of weekly problems for high school students. Check it out!

The topic of induction came up quite a few times this spring at the Girls’ Angle club, so next comes an article on this widely used proof technique.

This issue’s Learn by Doing features irrational numbers and culminates in a series of problems that let you reconstruct a proof of the irrationality of $\pi$ due to Charles Hermite.

Anna tackles one of Prof. Alexandrova’s weekly problems for high school students in Anna’s Math Journal, finding 3 different ways to solve the problem, which is to compute $\cos 72^\circ \cos 36^\circ$. Can you find your own solution?

Next comes our 4th installment on the derivative where we find the derivatives of the basic trigonometric functions. The way we deduce the derivative of sine is similar in spirit to the way we showed that the area under one hump of a sine curve is exactly 2.

Since this is our June issue, we include the 2015 Summer Fun problem sets. This batch contains problems pertaining to telescoping series (by Fan Wei), induction, the symmetric group (by Noah Fechtor-Pradines), and derivatives.

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!