We open with the concluding half of our interview with Draper Labs mathematician Erin Compaan. Dr. Compaan received her doctoral degree in mathematics from the University of Illinois Urbana-Champaign under the supervision of Nikolaos Tzirakis. She was a National Science Foundation Postdoctoral Fellow in Mathematics at the Massachusettes Institute of Technology prior to joining Draper Labs. In this second part, you can get a glimpse into one of Dr. Compaan’s hobbies: oil painting.
Deanna Needell has been organizing a major effort to apply mathematics to COVID-19 matters, and in this issue’s installment of Needell In The Haystack, she gives us a brief summary of these efforts. She outlines quite a number of ways data science can be applied to combating this dreadful pandemic. Perhaps a reader will be inspired to join that effort?
Next up is an intriguing article by Antonella Catanzaro, Jaemin Feldman, Mika Higgins, Bradford Kimball, Henry Kirk, Ana Chrysa Maravelias, and Darius Sinha, 7 eighth graders at the Buckingham, Browne, and Nichols Middle School. They merged algorithms and number theory by asking: What is the least expensive path through n cities, labeled 1 through n, starting at city 1 and allowing multiple visits to a city, if the cost to travel between city a and b is the least common multiple of a and b? In their quest for an answer, they unearthed a number of curious properties of “complete optimal paths” and taught themselves how to program in Python. There remain tantalizing mysteries to prove. Can you prove them?
One of their discoveries is that certain complete optimal paths have the structure of a multi-decker open-faced sandwich, hence the cover illustration, which was drawn by Mika Higgins.
This issue is the third in a row with student work, and we’d love to publish more! The Girls’ Angle Bulletin serves as a venue for students to showcase their mathematical work that goes beyond the classroom.
Emily and Jasmine are surprised by an email from Prof. Noam Elkies of Harvard University. In the previous issue, they proved the following theorem:
The ZigZags Theorem (Emily and Jasmine). Let n and m be distinct positive integers. Let a rectangle be crisscrossed by an n-zigzag and an m-zigzag, each bouncing back and forth between the top and bottom edges. Then the region of the rectangle below both zigzags, the region above both zigzags, and the region between the two zigzags split the rectangle exactly in thirds.
However, their method of proof, which involved explicit computation of the areas of all parts of the pattern created by two zigzags, did not offer much by way of explanation. Prof. Elkies found an alternative proof that provides such an explanation.
The Emily and Jasmine series is fiction, however the theorem is real, and was discovered in the summer of 2017 by the author along lines that closely resemble the fictional development in the series. Surprised and amused by the result, the author challenged a number of his math friends to prove it. After telling Prof. Elkies, hours later, Prof. Elkies sent the author an email which forms the centerpiece of this last installment in the zigzags saga of Emily and Jasmine. The purpose of the Emily and Jasmine series is to illustrate how mathematics is created with the hope that a reader might be inspired to create some math herself. That is, instead of presenting mathematics as a body of known results, in the Emily and Jasmine series, math is presented in a way in which it could plausibly be discovered or created as Emily and Jasmine create mathematics out of nothing but their minds.
We conclude with some Notes from the Club, which are authored by our Head Mentor Grace Work.
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!