## Girls’ Angle Bulletin, Volume 13, Number 3

Our cover features a tessellation by two nonconvex tiles designed by Katherine Dawson. More on her in a bit.

We open with the third part of a multi-part interview with mathematician Dr. Kristin Lauter, a professor at the University of Washington and a principal researcher at Microsoft Research. In this segment, Dr. Lauter discusses more recent develops in cryptography and how quantum cryptography might affect security. She also discusses the differences between academia and industry.

Next up, an article from student Marlie Kass who gives us the low down on the mathematics lurking behind a contest problem from the Mathematical Association of America’s AMC 12 series. In particular, she shows that the contest problem is an application of Bézout’s lemma. Bézout’s lemma is important because it tells us what numbers are invertible, modulo n.

This semester, one of our fifth grade members, Katherine Dawson, got really excited about tessellations and ended up designing an entire tessellating font, not just for the letters, but also for the digits. Her entire font is shown here as well as an indication of how each character can be used to tile the plane. Special thanks to Girls’ Angle mentors Amy Fang, Adeline Hillier, and Elise McCormack-Kuhman for very rapidly preparing computer graphic versions of Katherine Dawson‘s work for the Bulletin.

Next, we present two beautiful facts about Pascal’s triangle for you to meditate on and figure out. Both facts involve overlaying one Pascal’s triangle over another, hence the subtitle: Pascal on Pascal.

Emily and Jasmine further their understanding of partitions of rectangles created by regular zigzags.

Hyperia gets her pet ant to walk about the surface of a hypercube as we watch its shadow to help us improve our understanding of the fourth dimension, and this is followed by a Learn by Doing on 4D polytopes. If you’ve ever been curious about the 4D versions of the Platonic solids, but haven’t had a chance to get around to thinking about them, check out this problem set. You’ll find each regular 4D polytope or its dual here.

We close with a few 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!

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!