## Girls’ Angle Bulletin, Volume 11, Number 2

You could call this issue an ode to the triangle because half the content pertains to that most basic of geometric shapes, including the cover.

However, we open with an interview with UCLA Professor of Mathematics Deanna Needell. One of Prof. Needell’s mathematical interests is about how to get accurate views of things with less information, such as getting useful MRI scans in less scan time.

Next up is a nifty way to introduce vectors via partition functions by a group from Williams College, led by Pamela E. Harris. They motivate the whole concept by imagining a fictitious martian currency which behaves just like our dollar, except that there’s more than one unit of currency and they cannot be interchanged. The setup inevitably leads them to begin computing what is known as Kostant’s partition function for $A_3$. In fact, the authors dedicate the article to the memory of Bertram Kostant who passed away earlier this year.

Inscribed equilateral hexagons in an isosceles right triangle.

Milena Harned and Miriam Rittenberg are back explaining some results they found and proved this past summer about inscribing equilateral hexagons in triangles in such a way that every side of the triangle is flush with at least one side of the hexagon. In fact, for every triangle, they found a continuous family of such equilateral hexagons and they “rotate” about inside the triangle. You can explore these inscribed equilateral hexagons using a JavaScript app on the Girls’ Angle website.

Girls’ Angle mentor Ashley Wang pays tribute to triangles through her Math Buffet.

After an installment of Meditate to the Math (which asks you to interpret Sierpinski’s triangle as a sequence of binary numbers and contemplate its patterns), we present a self-referential test created by four Girls’ Angle members: Ghost Inthehouse, HolAnnHerKat, Katnis Everdeen, and Shark Inthepool. Earlier this fall, they solved Jim Propp’s self-referential multiple choice test and enjoyed it so much, they wanted to create their own. Their work was primarily overseen by Girls’ Angle mentor Rachel Burns.

Emily and Jasmine’s epic search for nice triangles comes to a heady conclusion. They succeed in putting all the pieces of the puzzle together to get a fairly complete classification of triangles with various numbers of integer side lengths and angles that measure rational multiples of $\pi$. Their journey took them through some lattice combinatorics, rational parameterizations of curves, and some basic Galois theory and a study of the values of cyclotomic polynomials at the square root of -1. And it all began with a fake triangle.

We conclude with some notes from the club.

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!

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