Girls’ Angle Bulletin, Volume 19, Number 3

Posted on February 28, 2026 by girlsangle
Cover of Girls' Angle Bulletin, Volume 19, Number 3

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

The interview for our 111th issue is with Catherine Roberts. Roberts is a professor at the College of the Holy Cross. She earned her doctoral degree in applied mathematics and engineering sciences and served as the Executive Director of the American Mathematical Society (2016-2023).

Five current high school students at the Buckingham Browne & Nichols school studied ice hockey shot angles when they were in 8th grade. They began with a 2D model and rediscovered the fact that the locus of points P such that the measure of \angle APB is constant, where A and B are distinct fixed points in the plane, form part of a circle that passes through A and B. Then, they moved into the third dimension and modeled the hockey goal as a rectangle instead of a line segment. Here, they employed spherical angle and created the analogous plot of loci of constant spherical shot angle on net, using a rink with dimensions corresponding to those of the recently used 2026 Olympic rink in Milan, where the US Women’s and Men’s teams both won gold. If you’ve not thought about spherical angle before, it is a measure of the fraction of a sphere that the projection of the goal mouth onto said sphere occupies. The formulas for the areas of a spherical triangle and quadrilateral are quite beautiful. See if you can figure them out yourself. If not, check out their paper!

Image
Drawing by Hanna Mularczyk

Next, we launch a new comic strip by MIT graduate student and Girls’ Angle mentor Hanna Mularczyk, “Bea and the Sea.” The first installment teases you with a secret code to decipher. I can’t wait to see what adventures Bea embarks upon in future installments!

Mathematical adventures are filled with mystery, excitement, and, yes, dark periods. In “Hyperball Volumes,” I give an account of an adventure that 9 eighth graders at the Buckingham Browne & Nichols school embarked upon this past fall and winter: A quest for the formulas for the hypervolumes of the hyperballs. Like many mathematical adventures, some mysteries were resolved, but others remain. Can you resolve the ones that remain?

In Members’ Thoughts, we give an overview of a surprising and beautiful theorem due to Girls’ Angle members Milena Harned and Iris Liebman. The two were playing around with line arrangements when they somehow noticed that the set of lines of the form Ax + By = 1 where A and B are integers satisfying -N \le A \le N and -N \le B \le N for some fixed N and (A, B) \neq (0, 0) forms a pattern of polygons in the plane completely devoid of pentagons, hexagons, heptagons, and, indeed any polygon with more than 4 sides! Note that for N = 10 this pattern consists of 440 lines pointing in 128 different directions and contains 58,577 polygons (of which 29,516 are triangles and 29,061 are quadrilaterals). If you took a random set of 440 lines (according to some typical distribution such as using a Gaussian for the coefficients A and B in the equation Ax + By = 1, you would expect to find many, many pentagons.

Here’s an illustration of the line arrangement with N = 4:

Image

Look carefully and you’ll see that, indeed, all the polygons are triangles or quadrilaterals!

Iris and Milena prove their theorem in a well written paper recently published in La Matematica, the Journal of the Association for Women in Mathematics. (This is the third professional publication on work done at Girls’ Angle, although the referee process took almost 4 years and both authors are now in college.) Although the only prerequisite for understanding their paper is Algebra 1 (all you need to know is that Ax + By = 1 is the equation of a line), their proof becomes rather subtle and tricky!

We conclude with 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!

Posted in math, Math Education | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 19, Number 2

Posted on December 31, 2025 by girlsangle
Cover of Girls' Angle Bulletin, Volume 19, Number 2.

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our 110th issue opens with the concluding half of our interview with University of Florida graduate student in mathematics Fatima Akinola. In this half, Fatima tells us more about her mathematics and leaves readers with a number of fun math questions to puzzle out that are examples of the kinds of things she thinks about in her own work.

Robert Donley adds another installment to his path counting saga with a look at generating functions associated to conjoined compositions.

Next, Emily and Jasmine resolve the mystery that confronted them in the previous issue while exploring the Taylor series for the tangent function. Since there mystery involved sums of entries in a triangle of numbers akin to Pascal’s triangle, they first attempted to settle the mystery by using induction and algebra. However, that quickly became unappetizing. In the end, they resolved the mystery by related everything back to the tangent function.

Girls’ Angle has been working with girls in a new math club organized by Prof. Fadipe-Joseph Olubunmi of the University of Ilorin in Nigeria (which is, coincidentally, where our interviewee is from). They inspired a question about bracelets which forms the topic of the latest contribution from Lightning Factorial. The cover illustrates all 50 different bracelets one can form using 12 beads total, with 6 black and 6 red.

We conclude with Notes from the Club which includes a sampling of problems from our traditional end-of-session Math Collaboration, which was designed this time by Girls’ Angle mentors Yaqi Li, Hanna Mularczyk, and AnaMaria Perez.

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!

Posted in math, Math Education | Tagged , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 19, Number 1

Posted on October 31, 2025 by girlsangle
Cover of Girls' Angle Bulletin, Volume 19, Number 1

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our 109th issue opens with an interview with University of Florida graduate student Fatima Akinola by Wellesley College undergraduate Elsa Frankel. Fatima was raised in Nigeria and came the United States for college. In this first part, Elsa asks Fatima about her upbringing and how she got into mathematics. They also discuss life as a graduate student in mathematics and the kinds of opportunities and support that exists for graduate students.

Next, Emily and Jasmine pick up where they left off in their journey to find the Taylor series for the tangent function. They explore properties of the polynomials they defined from the last part which appeared in Volume 18, Number 4. In the process, a mystery falls into their lap. The mystery can be stated this way: Create a triangular arrangement of numbers as shown below. (The black numbers are the entries in the triangular arrangement.) The orange numbers are factors by which the number at the foot of the arrow contributes to the number pointed to. For example, the 11 in the fifth row of black numbers is obtained by multiplying the 4 and the 1 in the row above by 2 and 3, respectively, and adding these results together. Notice the pattern created by the orange numbers. The mystery is to prove that in the odd-numbered row 2r+1 (i.e., the ones that do not begin with a 0), the sum of the entries in that row is 2^r times the first entry in that row. For example, in row 5, the sum is 4 + 0 + 11 + 0 + 1 = 16, and 16 is 2^2 times 4, its first entry.

triangular array o fnumbers

Robert Donley explores anti-magic squares in his continuing exploration loosely based on path counting.

Then, Addie Summer picks up where she left off exploring the k-dimensional faces of the n-dimensional hypercube. She finds formula for their numbers and describes two of them in detail, namely, the objects known as the rectified 5-cell and the birectified 5-simplex.

We conclude with Notes from the Club which includes a brief summary of a special presentation to the club by Ila Fiete, a professor of brain and cognitive sciences at MIT’s McGovern Institute.

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!

Posted in math, Math Education | Tagged , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 6

Posted on August 31, 2025 by girlsangle
Cover of Volume 18, Number 6 of the Girls' Angle Bulletin.

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our 108th issue opens with an interview with the Distinguished Professor in Science and Engineering and Professor of Mathematics at the University of Southern California, Los Angeles, Greta Panova. Greta describes how she got into math and touches on the role of math competitions in her life, among other things. Greta went to high school in Bulgaria, then graduated with two Bachelor’s degrees, one in Mathematics, the other in Electrical Science and Engineering, from the Massachusetts Institute of Technology. She received her doctoral degree from Harvard University under the supervision of Richard Stanley. In addition to her mathematics, Greta takes amazing photographs from her hikes. Check them out on her website. This interview was conducted by Wellesley College undergraduate Elsa Frankel.

Mathematics is a mental activity. The mind creates abstract structures and explores their properties and their relationship to other abstract structures. In school, however, the focus in math class has been on conveying the structures that others have created and explored, and little time, if any, is allotted to allowing students to participate in the process of creating mathematics. It would be analogous to a painting class where the students, instead of making paintings, spend their time looking at other people’s paintings. If you were to enroll in a painting class and found out on the first day that you wouldn’t be doing any painting, but, instead, you’d be looking at and analyzing other people’s paintings, would you stay in the painting class? I suppose some might stay, but it’s easy to imagine that many would find that approach boring and want to play with the brushes and paints. The same is true in mathematics, except that today, kids who find math class boring because they’d rather play with the math, don’t have that option and give up on math before they ever realize that math can be every bit as creative as a painting class.

And some youth have a real knack for creating math, like Caitlin Cunjak, whose adventure in Fibonacci land is described in this issue’s Member’s Thoughts. Whatever Caitlin explores, she leaves a trail of beautiful mathematical creations. One of the highlights of her recent journey was the discovery of a sequence of matrices whose determinants give the Fibonacci numbers and whose inverses exhibit intriguing patterns, enough for her to deduce the inverse without having to employ the matrix inverse formula. Although this matrix has already appeared in print, she joins good company, for it appeared in Volume 1 of Donald Knuth’s The Art of Computer Programming.

Next, Robert Donley shows us how to create a regular graph given a linear code with some constraints. If you like coloring the edges of graphs, this installment of his ongoing Path series is for you!

We conclude with solutions to this year’s batch of Summer Fun problem sets.

By the way, both articles by 8th graders in the previous issue have led to some new sequences on the On-Line Encyclopedia of Integer Sequences! Check them out: https://oeis.org/A385812, https://oeis.org/A386525, and https://oeis.org/A156301.

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!

Posted in math, Math Education | Tagged , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 5

Posted on June 30, 2025 by girlsangle
Cover of Girls' Angle Bulletin, Volume 18, Number 5

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our 107th issue opens with an interview with University of Rochester Mathematician Amanda Tucker. Amanda earned a Bachelor of Science from the Massachusetts Institute of Technology and received her doctoral degree from the University of California, San Diego. At Rochester, she also serves as Assistant Director of Undergraduates Studies. She is the Founding Director of GirlsGetMath@Rochester as well as the founder of Flower City Math Girls.

Following the interview are two articles both written by 8th graders at the Buckingham Browne & Nichols Middle School in Cambridge, Massachusetts.

In the first, authors Anna Gorman-Huang and Evelyn Marks present their findings on how to best approximate powers of 2 using powers of 3. There investigation led them to define a refinement of rounding, which the dubbed “Break Point Rounding.” Their work also provides a way to approximate the numerical values of various logarithms. For example, one implication of their work is that

\displaystyle{\log_3 2 = \lim_{N \to \infty} \frac{\#\{n \in \{1, 2, 3, \dots, N \} ~|~ \exists k \in {\Bbb Z} \text{ such that } \frac{1}{2} \le \frac{3^k}{2^n} < 1\}}{N}}

For example, when N = 10000, the fraction within the limit expression evaluates to 0.6310, whereas \log_3 2 \approx 0.63092975357....

In the second, Helena Lai and Margot Reinfeld introduce what they call “LR” numbers. They decided to play with dice, but not just any dice. They decided to play with a die that can come up any positive integer. They studied the outcomes generated by taking the product of two such die rolls. In the process, they came up with a couple of intriguing conjectures, one of which is about the largest factor of a number that is less than or equal to the number’s square root. That is, define h(n) to be the largest divisor d of n such that d \le \sqrt{n}. (See sequence A033676 on the On-Line Encyclopedia of Integer Sequences.) Lai and Reinfeld essentially conjecture that, on average, h(n) < h(n+1) half the time and h(n) > h(n+1) half the time. (Note that h(n) is never equal to h(n+1), except when n = 1, 2.

Next, Robert Donley’s continues his exposition on Latin squares and 1-factorizations of regular bipartite graphs with his 21st installment on counting. Do you know how many 5 by 5 Latin squares there are? Read Robert’s article to find out!

In keeping with tradition, we include this year’s batch of Summer Fun problem sets. This summer, we have two, both authored by MIT graduate students, one on intertwined polynomials and one on the game “The Mind.”

We conclude with some 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!

Posted in math, Math Education | Tagged , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 4

Posted on April 30, 2025 by girlsangle
Cover of Girls' Angle Bulletin, Volume 18, Number 4

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our 106th issue opens with the conclusion of our three part interview with math and science journalist Erica Klarreich. Thank you so much, Erica, for doing this interview!

Next, Robert Donley’s 20th installment on counting continues with more on semi-magic squares and the introduction of hypergraphs. This issue’s cover, like the last issue, illustrates hypergraphs connected to representatives of certain orbits of 6 by 6 semi-magic squares with line sum 3: Essentially, how many different ways are there to place 6 triangles into a hexagon in such a way that each vertex of the hexagon is a vertex of 3 of the triangles? (You are allowed to use the same triangle more than once.)

Emily and Jasmine embark on a new mathematical adventure, this time investigating the Maclaurin series for the tangent function.

Addie Summer extends her investigation of hypercube cross sections and stumbles upon a beautiful geometricization of Pascal’s triangle that consummates the relationship between the two iconic mathematical concepts.

For anyone just learning about logarithms, we provide a very brief basic introduction.

Lightning Factorial seeks the chocolate with the least amount of sugar that is still enjoyable in ChocoMath. If you do this experiment, let us know what you found to be the minimal amount of sugar you need before the chocolate becomes too bitter. Homemade chocolate is very easy to make, and since you control the ingredients, it can be a lot healthier than commercial products.

We conclude with some 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!

Posted in applied math, math, Math Education | Tagged , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 3

Posted on February 28, 2025 by girlsangle
Cover of Girls' Angle Bulletin, Volume 18, Number 3

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Our latest issue opens with the middle part of our 3-part interview with math and science journalist Erica Klarreich. In this part, Erica touches on some of the challenges of writing about mathematics in particular and her writing process.

Robert Donley’s nineteenth installment on counting continues with circulant graphs and semi-magic squares. The content in his latest installment inspired the cover image. The cover also relates to Bezout’s lemma.

Emily and Jasmine think more about fractran, John H. Conway’s curious programming language where each command is a fraction. In this issue, they show that any algorithm that can be implemented on a standard computer can be implemented in fractran by producing the fractran code for a modular NAND gate. The NAND gate is a universal logic gate, which means that all logic gates can be built by composing NAND gates. If you’re unfamiliar with universal logic gates, turn to this issue’s Learn by Doing.

Addie Summer follows-up on her initial investigation into the symmetries of the hypercube by taking a closer look at certain cross-sections which happen to form a family of convex polyhedra for which Pascal’s triangle gives the number of vertices.

Lightning Factorial concludes with an introduction to some concepts that sprout when we take the leap from the finite to the infinite: specifically, Lightning defines the infimum, supremum, limit, and limit infimum and limit supremum.

We conclude with some 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!

Posted in math, Math Education | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 2

Posted on December 31, 2024 by girlsangle
Cover of Girls' Angle Bulletin, Volume 18, Number 2

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

For this issue, we have a very special interview with Erica Klarreich. Erica earned her doctoral degree in mathematics from the State University of New York, Stony Brook, then later shifted into math journalism where she has written on dozens of diverse mathematical topics with her characteristic combination of clarity and precision. She belongs to a class of journalists who both write well and understand math from the point-of-view of a mathematician.

In my opinion, writing about mathematics is a special kind of challenge. Mathematical ideas are abstract and exist only in the mind. While a small percentage of these abstract ideas lend themselves to graphic depictions, we know most math mainly through nonvisual properties. Yet, mathematicians are drawn to these abstract objects mainly because they perceive in them great beauty and elegance. Conveying this beauty and elegance without getting mired in technical details or creating misleading imprecisions is difficult, which probably goes far in explaining why mathematics remains relatively unpopular, but it is something Erica excels at pulling off. We recommend that you check out all of her pieces, which can be found in various publications, including the Atlantic, Quanta, Scientific American, and Wired.

Robert Donley’s eighteenth installment on counting continues with perfect 1-factorizations of graphs and Latin rectangles. In it, he discusses the unsolved problem of determining which complete graphs have perfect 1-factorizations. As of this writing, it is not known if the edges of the complete graph on 64 vertices can be partitions into 63 perfect matchings with the property that any two of the perfect matchings combine to form a Hamiltonian cycle.

Speaking of outstanding math communicators, this issue’s Emily and Jasmine is inspired by Siobhan Robert’s biography of John Conway. In that biography, Emily read about Conway’s computer language “fractran,” and she and Jasmine ended up writing a fractran program as they try to make sense of Conway’s claim that the fractions 17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, and 55/1 are a program that generates the prime numbers. For a graphic version of the output of Emily and Jasmine’s program, see this issue’s cover.

Image

Lightning Factorial concludes an exploration of cubic polynomials with a map of cubic polynomials with real coefficients whose roots sum to 0. This map is split into two regions: the cubic polynomials that have exactly one real root and the cubic polynomials that have three real roots. The two regions are separated by a boundary of cubic polynomials that have multiple roots. The tangent lines to the boundary have a particularly nice interpretation.

Next, Addie Summer works out the symmetry group of the n-dimensional hypercube.

We conclude with some 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!

Posted in math, Math Education | Tagged , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 18, Number 1

Posted on October 31, 2024 by girlsangle
Cover of Girls' Angle Bulletin, Volume 18, Number 1

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

We open with the second half of our interview with Boston University Professor of Mathematics Jennifer Balakrishnan. In the second part, she describes her collaborative work in algorithmic number theory. She refers to a beautiful article she wrote which we hope everyone reads: A Tale of Three Curves. She also discusses failure in such a wonderful way that I want everyone to read it, so here is an extended quote from the interview:

Perhaps I can share a story from when I was a postdoc.  I had the great fortune of working with Barry Mazur at Harvard.  We were discussing a computation that I had been trying, and it just didn’t work out, and he thought, and then he said, ‘Well, that makes it even more interesting, doesn’t it, when it doesn’t work out the way that you expect it to. That means that there’s something even deeper than what we thought was happening.’

And that really changed my viewpoint on mathematics.

Of course, Barry Mazur, I think he needs no introduction, but he made these wonderful discoveries in topology, and then moved on to number theory, and proved so many foundational, beautiful results. After Barry’s kind remarks, I realized that that sort of outlook is just so important—that you see not the fact that it didn’t work out, but rather the suggestion that there’s something deeper, and more interesting, fundamentally, out there…that it’s not a failure, but rather the chance that you might be able to uncover something that you didn’t even know was there.  And that, I think, is an important outlook, not only for mathematics, but for life itself.

– Jennifer Balakrishnan

Next, we present the mathematical journey undertaken by seven 8th graders at the Buckingham Browne & Nichols Middle School. Their journey began with a natural question of curiosity: What are the degree measures of the angles in a 3-4-5 right triangle? (You might react, the angle measures are just \arctan(3/4), \arctan(4/3), and 90^\circ. But this doesn’t actually answer their question!) They also succeeded in proving that the acute angles are an irrational number of degrees.

This group of 8th graders have produced numerous wonderful ideas, and another article, Any Takers?, presents a gambling game that they developed that is amusing to think about. You could also probably make a lot of money on it!

Robert Donley’s seventeenth installment on counting continues with regular coloring of hypercubes.

One of our members has been studying group theory, and so we included a Learn by Doing on quotient groups and normal subgroups.

We conclude with some 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!

Posted in math, Math Education | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

Girls’ Angle Bulletin, Volume 17, Number 6

Posted on August 31, 2024 by girlsangle
Cover of Girls' Angle Bulletin, Volume 17, Number 6

The electronic version of the latest issue of the Girls’ Angle Bulletin is now available on our website.

Before you look on the inside front cover to see what the cover image represents, what patterns do you make out in it?

In this issue, we present the first installment of an interview with Boston University Professor of Mathematics Jennifer Balakrishnan. In this first part, we Jennifer traces her history from being raised in Gaum to becoming an expert in algorithmic number theory and arithmetic geometry. You may already have thought about algorithmic number theory. Perhaps you wrote a computer program to generate Pythagorean triples, for example? Jennifer and her team of mathematicians push the bounds on how computers can be combined with mathematics to productive ends.

Robert Donley’s sixteenth installment on counting continues his exposition on permutation matrices and matchings in graphs. Each one of Bob’s articles provides a wealth of raw materials which we hope you play with. There are plenty of discoveries to be had, and we hope you make some of your own!

Lightning Factorial continues exploring cubic polynomials. This time, armed with an procedure for finding the roots of a cubic, Lightning delves into the structure of these roots and discovers a magnificent rotating equilateral triangle associated to any three real numbers.

We conclude with the solutions to this year’s batch of Summer Fun problem sets.

an infinite path

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!

Posted in math | Tagged , , , , , , , , , , , , , , | Leave a comment