## Math Intuition Test

After you make your intuitive guess, compute to find out the truth!

## Girls’ Angle Bulletin, Volume 10, Number 3

Volume 10, Number 3 opens with an interview with Sommer Gentry, professor of mathematics at the US Naval Academy. Prof. Gentry invented a system for optimizing kidney transplantation that positively. This interview was conducted by Girls’ Angle progam assistant Long Nguyen. As has been our practice, we truncate the interview in the electronic version. For the full version, please subscribe!

Next comes Villanova assistant professor of mathematics Beth Malmskog‘s concluding part of Quilt-Doku! Here she shows that a 5 by 5 row complete Latin square is impossible. Shown at right is a row complete Latin square of order 15. It remains an unsolved problem to determine if there are any row complete Latin squares of odd prime order.  In fact, it isn’t even known that there isn’t one of order 13. Can you prove it?

Test your area computation skills in Area Area. Can you solve these area problems in your head?

Anna B. continues to search for a combinatorial proof that the conjectured formula she found for the number of special tilings of a 1 by $\sqrt{2}$ rectangle is, in fact, valid. She remains stumped. Can you help her prove that the close-form formula she found is correct?

Emily and Jasmine continue their pursuit of triangles with 3 nice angles but only 2 sides of integer length at Cake Country where they run into Alison Miller, a Benamin Peirce and NSF Postdoctoral Fellow at Harvard University. Prof. Miller gives them a lot to chew on for next time! She also mentions Gauss’s Lemma, but doesn’t have time to prove it, so we provide an installment of Learn by Doing where you can prove the lemma for yourself.

The cover pertains to Addie Summer’s follow-up to her article on the quadratic formula. In this issue, she creates a graphical representation of monic quadratics and interprets properties of them geometrically. On the cover, the surface represents monic cubics with multiple roots. Specifically, it is the surface of points (bcd) in bcd-coordinate space such that the cubic $x^3 + bx^2+cx+d$ has multiple real roots. (Note that if a cubic with real coefficients has multiple real roots, then all of its roots are real.) This graph was created using MATLAB, a powerful suite of math software created by MathWorks. MathWorks has been a valuable sponsor of the Girls’ Angle Bulletin for several years.

For fun, we offer a self-referential true/false quiz that was inspired by a self-referential multiple choice test created by Jim Propp.

Finally, we conclude with Notes from the Club, which contains a description of one of our more versatile and popular games: Describe that Drawing.

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!

## Girls’ Angle Bulletin, Volume 10, Number 2

Volume 10, Number 2 opens with an interview with Doris Schattschneider, professor emerita of mathematics at Moravian College. Among many other things, Professor Schattschneider was the first woman to serve as editor of the MAA’s Mathematics Magazine. This interview was conducted by Girls’ Angle summer intern Sandy Pelkowsky. As has been our practice, we truncate the interview in the electronic version. For the full version, please subscribe!

The cover is a picture of the function $x^2 + y^2$, modulo the prime number 503. For more examples and an explanation of how the image was made, check out this issue’s Mathematical Buffet.

We feature a contribution from Villanova assistant professor of mathematics Beth Malmskog, Quilt-Doku! Prof. Malmskog shows how she went from a quilting friend’s request to unsolved problems in mathematics. She blogs for the American Mathematical Society – check it out!

We’d also like to take special note of a member contribution in Member’s Thoughts.  Here, π takes us along on her derivation of the volume of a regular n-simplex. An n-simplex is an n-dimensional generalization of the triangle.

Emily and Jasmine continue their pursuit of triangles with 3 nice angles but only 2 sides of integer length. While they make some progress in their investigation of the minimal polynomials of cosines of nice angles, the journey begins to appear rather daunting!

Last issue, Anna B. found a recursive formula for the number of special tilings of a 1 by $\sqrt{2}$ rectangle. In this issue, she manages to guess the closed-form formula, but is unable to prove it. Can you help her prove that the close-form formula she found is correct?

Addie Summer explains how she discovered the quadratic formula. In the process, she shows that the algebraic technique known as “completing the square” corresponds to a natural geometric idea: shifting the parabola sideways so that it is symmetric about the y-axis.

In Notes from the Club, we mention a few of the things that have been happening at the Girls’ Angle club and give a sampling of problems from our traditional end-of-session Math Collaboration.

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!

## Chebyshev Polynomials of the First Kind

This animation illustrates the connection between roots of the Chebyshev polynomials (of the first kind) and the vertices of a regular polygon inscribed in the unit circle centered at the origin. For a still image, see the cover of the Volume 8, Number 5 of the Girls’ Angle Bulletin.

## Potatoes are made of ducks

Recently at the Girls’ Angle Club, we mentioned that from a contradiction, one can prove anything. One of our members, Barry Allen (pseudonym!), challenged us to prove that potatoes are made of ducks given that potatoes are made of wood.

## Girls’ Angle Bulletin, Volume 10, Number 1

Volume 10, Number 1 opens with an interview with Dr. Brandy Wiegers, an assistant professor of mathematics at Central Washington University and associate director for the National Association of Math Circles.  This interview was conducted by Girls’ Angle summer intern Sandy Pelkowsky. As has been our practice, we truncate the interview in the electronic version. For the full version, please subscribe!

The cover features an image of an opened Quintetra assembly by Jane and John Kostick. Jane visited Girls’ Angle last month and led the girls in an exploration of tetrahedra, cubes, and rhombic dodecahedrons. For more on the Quintetra assembly, please see Volume 7, Number 4 of the Girls’ Angle Bulletin.

After the interview, we offer 3 theorems to meditate upon in Meditate to the Math. All 3 theorems involve the construction of dropping a perpendicular from a point to a line, and, although it might be a challenge, all 3 theorems can reasonably be proven without use of scratch paper – just sitting comfortably, observing, thinking, meditating.

Next up is the concluding half of Prof. Helen Wilson‘s article on chocolate flow. This half is considerably more mathematically involved than the first half. In it, Prof. Wilson gets into the details of scaling analysis by leading us through an example involving liquid chocolate. It’ll help if you’re familiar with calculus. Just don’t be intimidated by the big partial differential equations that govern fluid flow! The whole point of the article is to show how to tame such a massive equation.

Emily and Jasmine return to their pursuit of triangles with 3 nice angles but only 2 sides of integer length. They decide to embark on an investigation of the minimal polynomials of cosines of nice angles.

Anna B. follows through on a question that sprouted up in the last issue: how many special N-tilings are there of a 1 by $\sqrt{2}$ rectangle?

Addie Summer goes crazy (well, in a way) and counts some familiar sets in a complicated way, and is rewarded with beautiful identities involving binomial coefficients.

We conclude with Notes from the Club, featuring just a few of the things that have been happening at the Girls’ Angle club so far this semester.

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!