## Girls’ Angle Bulletin, Volume 15, Number 2

The cover shows all 35 ways to tile a 4 by 4 rectangle with 1 by 1 and 2 by 2 tiles, as organized according to a scheme dreamed up by a group of 8th graders at the Buckingham, Browne, and Nichols Middle School in Cambridge, MA. The number of such tilings of a 4 by N rectangle has been well-studied and a number of recursion formulas are known. But one recursion formula was noted by Schneider without proof or reference:

$S_n = 2S_{n-1} + 3S_{n-2} - 2S_{n-3}$,

where $S_n$ is the number of ways to tile a 4 by n rectangle with 1 by 1 and 2 by 2 tiles. These 8th graders succeeded in proving it, and in just a few clever lines! Details are in their article on page 8.

In Part 1 of our interview with Professor Tullia Dymarz, Tullia describes the lamplighter group and a pipe cleaner model she made of one of its Cayley graphs. If you were interested in trying your hand at building the pipe cleaner model but haven’t learned about Cayley graphs yet, check out this issue’s Learn by Doing to get going. In Part 2 of Tullia’s interview, she tells us more about her research process and describes one of her own discoveries which concerns which Cayley graphs of different lamplighter groups are quasi-isometric.

One point we try to emphasize in the Bulletin is that doing math is just a matter of being curious, coming up with questions that can be analyzed rationally and abstractly, and trying to answer them. The mathematical universe is so enormous with so much unexplored territory that if you start doing this, it will not be long before you come upon something new. It is an astonishing journey, full of surprises and awesome beauty. For example, there was the time when Emily and Jasmine stumbled upon their “Zigzag” theorem. (See pages 16-20 of Volume 13, Number 3 and pages 20-26 of Volume 13, Number 4, or read this earlier blog post. Although a fictionalized account, the story does closely describe how the theorem was actually born.) In our ongoing attempt to further this point, we follow Lightning Factorial’s thoughts on 2022 and point out the math that oozes out from thinking about that number’s properties in All That Math.

Anna Ma, who has taken over The Needell in the Haystack from originator Deanna Needell, addresses a super important question in data science: What do you do if your data is incomplete? It is an extremely common predicament to find oneself in. She begins the discussion, but it is an active area of research.

We conclude 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!

Also, the Girls’ Angle Bulletin is a venue for students who wish to showcase their mathematical achievements that go above and beyond the curriculum. If you’re a student and have discovered something nifty in math, considering submitting it to the Bulletin.

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!