## Girls’ Angle Bulletin, Volume 10, Number 4

Volume 10, Number 4 opens with an interview with Nalini Joshi, Professor of Mathematics in the School of Mathematics and Statistics at the University of Sydney. Prof. Joshi received her doctoral degree from Princeton University. She studied differential equations. The cover represents the iterates of an integrable third-order difference equation that arose out of joint work between her and Dr. C.-M. Viallet of CNRS and Sorbonne Universités. Dr. Viallet created the cover image.

In the 10th installment of In Search of Nice Triangles, Emily and Jasmine apply the knowledge they learned from Prof. Alison Miller from Part 9 and succeed in finding the minimum polynomials of the cosines of “nice” angles, a big step toward their goal of classifying all triangles that have 3 “nice” angles and 2 sides of integer length.

In Anna’s Math Journal, Anna gives in to the temptation of the generating function and uses it to prove her conjecture about the number of “special” tilings of a 1 by $\sqrt{2}$ rectangle.

Next up, Milena Harned and Miriam Rittenberg explain different ways of counting the number of ways a game of NIM can be carried out. In this first half, they find explicit formulas when the game begins with two piles, one of which has a small number of counters. In the final half, which will appear in June, they will examine the asymptotics of the general 2-pile case.

Detail from Vermeer’s Art of Painting

Recently at the Girls’ Angle club, some members have been studying perspective drawing and practicing the theory by making drawings of geometric objects such as a checkerboard, like the one in the floor of Vermeer’s Art of Painting. This issue’s Math In Your World shows how the harmonic mean lurks within this topic. In fact, there’s a lot of beautiful mathematics in perspective drawing.

Milena Harned decided to generalize an idea she found on the 2002 American Invitational Mathematics Exam I. Along the way, she found some polynomials that relate to the famous way of obtaining the Fibonacci numbers from Pascal’s triangle shown at left.

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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