## Girls’ Angle Bulletin, Volume 7, Number 5

A paraboloid of revolution adorns the cover. Anna investigates cross sections of paraboloids in this issue’s Anna’s Math Journal. It sure feels like Anna is embarking on an interesting mathematical journey with this new topic. We hope you’ll be inspired to follow-up on her work.

However, first up is the concluding half of our interview with University of Oregon Professor Emerita Marie Vitulli. Read some of the ways she thinks gender bias in mathematics can be countered.

Next, Akamai Technologies computer scientist Kate Jenkins discusses algorithms that find the “maximal subsequence” of a sequence.  Her first part closes with an interesting challenge. Can you find a solution to her challenge before she gives it in the next issue?

Brit Valeria Golosov presents a fictional account of how she imagines that Brahmagupta derived his famous formula for the area of a cyclic quadrilateral. Valeria is entering her final year of secondary school in London.

This issue’s Math In Your World was specifically requested by Vida John. We love receiving content requests from members and subscribers. This Bulletin is written for members and subscribers and members and subscribers are welcome to control Bulletin content by emailing us comments and suggestions.  Please don’t be shy about emailing us about anything to do with math! We also welcome and encourage all members and subscribers to send in solutions to the Summer Fun problem sets. We might even publish your solution in the Bulletin.

This summer’s batch of Summer Fun problem sets address magic squares, mass points, quadratic reciprocity, and permutations. Contributors include Johnny Tang and Cailan Li, both recent high school graduates who will be heading to college this coming fall. The central theme of Volume 7, Number 3 of the Bulletin was the concept of center of mass which underlies the technique of mass points. In that issue, we didn’t have enough room to include many problems to practice the technique. So that’s one reason why we included a problem set on mass points. The problems range from introductory level to some that will hopefully entertain those experienced in the technique. Cailan’s problem set takes readers from the rudiments of modular arithmetic all the way through a proof of Gauss’s Law of Quadratic Reciprocity, following a proof by D. H. Lehmer. The set on permutations culminates with a result of Zolotarev that links signs of certain permutations to the Legendre symbol introduced in Cailan’s problem set.

To whet your appetite, suppose AB, and C are the angle of a triangle. Can you prove that

$9 > 3 + 2(\cos 2A + \cos 2B + \cos 2C) \ge 0$

with equality if and only if the triangle is equilateral? For a spiffy way to prove this, check out the Summer Fun problem sets!

We conclude with a brief account of a wonderful field trip we took to MIT’s Department of Aeronautics and Astronautics, which was generously organized by Professor Karen Willcox,

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!