...And Now for Some Math on Pi Day!

Curious about more math this Pi Day? Here’s the problem we included in this year’s Pi Day card:

Problem:

Two logicians (A and B) each secretly pick a whole number from 1 to 30, inclusive. They have the following conversation:

A: “Is your number double mine?”
B. “I don’t know. Is your number double mine?”
A. “I don’t know. Is your number half mine?”
B: “I don’t know. Is your number half mine?”
A: “I don’t know.” 

B: “I know your number.”

All the statements are true. What is A’s number and how did B know?

Solution:

Let’s break this down into what everybody knows after each exchange.

A: Is your number double mine? B: I don’t know.

If B’s number is odd he could say, “No, my number is not double yours.” But instead he says he doesn’t know, so B’s number must be even.

At this step B’s number is one of the following 2, 4, 6, …, 30. A’s number is still anything from 1, 2, …, 30.

B: Is your number double mine? A: I don’t know. 

This definitely tells us that A’s number is at least even too, but it actually tells us more. Because A already knows B’s number must be even, so A’s number must be double an even number (which is another way to say it must be a multiple of 4).

So at this point both logicians know that:

B’s number is one of these: 2, 4, 6, ..., 30 and A’s number is one of these: 4, 8, 16, 20, 24, 28. 

A: Is your number half mine? B: I don’t know.

Now B knows that the largest A’s number could be is 28, so if B’s number is greater than 14 he could say with certainty that no, his number is not half of A’s. But he says “I don’t know,” so now we know that B’s number is 14 or less.

Now both logicians know that:

B’s number is one of these: 2, 4, 6, 8, 10, 12, 14, and A’s number is one of these: 4, 8, 16, 20, 24, 28.

B: Is your number half mine? A: I don’t know.

A knows that the largest B’s number could be is 14, so if A’s number was larger than 7, A would know that their number was certainly not half B's. However, A says I don’t know, so their number must be equal to or less than 7. But we already knew that A’s number was 4, 8, 16, 20, 24, or 28. Only one of these options is less than or equal to 7, and that is 4.

So now both logicians know that A’s number is 4. 

WANT TO LEARN ABOUT the pizza theorem?

Check out our Pi Day blog post!

The Pizza Theorem: How Sharing a Pizza Got Even More Fun!

Zereena at Family Lunch in 2016

Pizza holds a special place in our hearts at BEAM. From the very beginning, through the challenges of COVID, we’ve shared pizza (even when we could only do it virtually) and built community together. So this Pi Day we’re spotlighting the humble pizza pie. Since it’s impossible to share an actual pizza with you, dear reader, we’re doing the next best thing — sharing a theorem about sharing pizza, the aptly named pizza theorem.

The pizza theorem says that if a pizza is cut 4 times through a point P into 8 slices of equal angle 45°, and slices are alternately topped with pepperoni and mushrooms, then the total area of the pepperoni slices equals the total area of the mushroom slices.

Note that the point P can be any point within the pizza.

If we ordered a half-and-half pizza and this arrived, we would be flabbergasted, but we'd have to ask ourselves: is there really the same amount of pepperoni and mushrooms? The longer we look at the picture above, the less sure we are that it is true at all.

The pizza theorem belongs to one of the most intriguing sorts of math problems — the statement is simple and straightforward, but it’s not obvious whether it’s true or not and the path towards proving it appears tricky, or even impossible.

Problems like these are responsible for entire fields and careers in pursuit of answers, and they also showcase one of the strengths of mathematics: that we can use logic to wade through the uncertainty, and arrive at what is, 100%, true.

To build some intuition about whether the theorem holds or not, let’s draw some examples. You see that you can create some pretty wild (potentially) half-and-half pizzas!

From the last example, it's not clear how you'd write a proof. So let's test the assumptions: what if you cut the pizza 2 or 3 times (instead of 4) into slices with equal angles? We can come up with examples with 2 or 3 cuts where the alternating slices definitely do not share the same value for combined area, so the theorem does not hold for 2 or 3 cuts. So, there's something special about making 4 cuts that makes the theorem hold. (In fact, it works with 4, 6, 8, etc. cuts.)

Proof with calculus and π

We'll share the proof from the article "Dividing a pizza into equal parts — an easy job?" by Professor Hans Humenberger of the University of Vienna. Most proofs are surprisingly complex, but here you can understand what is going on and the final answer actually includes pi (how perfect)! However, we have to warn you: this part gets technical and uses some calculus, so if that's not your thing, you might want to skim past!

A proof inside a proof:

To begin, we need a "lemma." Lemma is just a fancy way of saying "a proof within a proof," a little mini-fact that we'll use to prove our final fact. In fact, the word "dilemma" comes from the same root: "lemma" means premise, so a "dilemma" makes you cope with two premises!

Key Lemma: For every pair of orthogonal chords (segments a, b, c, d in Figure 7) in a circle of radius r, the following equation holds:

a2 + b2 + c2 + d2 = (2r)2

The Key Lemma (which looks suspiciously like the Pythagorean theorem) states that for each orthogonal (i.e., meeting at a right angle) pair of chords, the sum of squares of the lengths of the subchords equals the square of the diameter. A lovely (and relaxing) visual proof of this lemma can be found here: Four squares with constant area | Visual Proof | Squaring the segments. But let's make sure we have all the details of the proof.

Proof of the Key Lemma. The proof will rely on the fact that subchords a and b meet at a right angle and subchords c and d also meet at a right angle. 

We can consider the hypotenuse of the triangle with a and b as legs and then make a square with this hypotenuse as one of its sides (green square below). Similarly, we can make a square with the hypotenuse from c and d as one of its sides (pink square below).

There's another geometry theorem that will help us out here: The Angle of Intersecting Chords Theorem (see here) implies that the sum of the lengths of the green arc and the pink arc equals half the circumference of the circle. This means that if we rotate the green square and the pink square towards each other along the circle so that the two squares meet, the white arc of the circle contained within the green and pink squares will be half the circle. 

This is practically begging for us to apply the Pythagorean theorem, but for the Pythagorean theorem to give us the desired result, we need two things to be true:

  1. The orange line (that connects the corners of the green and pink squares) is a diameter. This is true because as stated above, the arc of the circle contained within the green and pink squares makes up half of the circle.

  2. The green and pink squares meet at a right angle. To see this is true, note that the intercepted arc of the angle formed by the green and pink squares’ sides is also exactly the opposite half circle (see point 1), which has angle 180 degrees. By the inscribed angle theorem, the angle of the intercepted arc is twice the angle of the inscribed angle in the circle, which means the angle between the green and pink squares is 90 degrees. 

We can then apply the Pythagorean theorem to the side lengths of the green and pink squares with the diameter of the circle to prove the Key Lemma:

(2r)2 = a2 + b2 + c2 + d2

Proving the Pizza Theorem (using the Key Lemma)

The Leibniz sector formula calculates the area of a pizza slice (in other words, a sector of a circle) based on the distances from the tip of the pizza slice to the edge of the crust (that is, the original circle). Written below is the formula when considering 45-degree slices for the pizza theorem, where r(𝜃) is the distance from the slice’s point to the outer crust at angle 𝜃. Here, angle = 𝜋/4 refers to the side that is clockwise from the angle = 0 side.

In the pizza below, consider the dark slices as the pepperoni slices. We can calculate the total area of the pepperoni slices as the sum of the area of the individual slices using the sector formula:

The right sum in the formula above can be grouped as:

Now we can use the incredible fact that for any given 𝜃, the four radii r1(𝜃), r2(𝜃), r3(𝜃), and r4(𝜃) are orthogonal to each other, which means that the initial “Key Lemma” holds for each 𝜃. This means that we have

This proves that the dark slices (aka, the pepperoni slices) make up half the total area of the pizza, which means the light slices (aka, the mushroom slices) must also make up half the total area. This proves the pizza theorem!

This is just one proof of the pizza theorem. This theorem has also been proven a few times via “proofs without words,” starting with a purely picture proof published in Mathematics Magazine in 1994 by Carter and Wagon. The idea of these proofs is to cut up the slices into smaller pieces, then match up congruent “mushroom” pieces to “pepperoni” pieces. The article above by Humenberger includes a great discussion on these proofs, and you can even visualize a dissection into smaller, congruent pieces via the awesome web app by Christian Lawson-Perfect at Proof without words of the pizza theorem.

We hope that you’ve had a scrumptious time proving the pizza theorem with us. Feel free to hit us up on social media with your favorite pictures of half-and-half pizzas!

Zoom Pizza Party in 2020

More Math

At BEAM, we love statements like the Pizza Theorem — the statement is simple and straightforward, but it’s not obvious whether it’s true or not and the path towards proving it appears tricky, or even impossible. These problems can grab your attention and get your mind racing. A few other math problems that are similar in this way (all coming here from number theory) include:

  • Goldbach’s Conjecture: Every even integer (greater than 2) can be written as the sum of two primes.

  • The Twin Prime Conjecture: There are infinitely many pairs of primes 2 apart from each other.

  • Fermat’s Last Theorem: There are no solutions to the equation a2 + b2 = c2, for positive integers a, b, c, and n with n > 2.

We’ve actually explored all of these problems here at BEAM, and Dan, our CEO, has given talks on the Twin Prime Conjecture in several classes. So if you are in need of more math to contemplate this Pi Day, one or all of these should give you plenty to chew on!

…and now for some Math on Pi Day

Check out this blog post!

A Look Back at an Outstanding Summer!

Mathematical Wins

At Summer Away (our program for rising 8th graders), students were exceptionally engaged both inside and outside the classroom. In particular, they spent many hours outside of instruction time solving Challenge Problems, weekly problems beyond their daily coursework completed in teams or on their own.

Want to try out a challenge problem for yourself? Here’s Oscar and Yanny’s favorite: “What is the digit sum of the product of the 94-digit number consisting of all 9’s and the 94-digit number consisting of all 4’s?” Let us know what you think!

When we asked students, What’s the longest time you spent working on a single problem this summer, the median response of students at Summer Away, Pepperdine, was 48 hours — hats off to their perseverance! The median student at this site also grew an incredible 22% in national ranking on a national math contest (which we use to measure problem-solving growth) over the course of the summer. We consider 10% growth a “great” result, so this was truly exceptional.

This summer at BEAM Discovery (our program for rising 7th graders) in New York City and Los Angeles, students eagerly tackled the 100 Problem Challenge (100 difficult, puzzle-like math problems that involve teamwork, pattern-finding, and strategy). Students at all three sites completed all the problems, earning an ice cream field trip! Consider this problem from the 100 Challenge: Fill in each of the hexagons (at right) with a positive integer so that the number in each hexagon is equal to the smallest positive integer that does not appear in any of the hexagons that touch it.

Learn more about the puzzle and its solution here.

When asked what she would tell another student about BEAM, Alice T said “I’ve never been this excited to do math, especially the 100 Problem Challenge.” 

A New Course

How do mathematicians know that a particular fact is true? For example, how do we know for certain that there are infinitely many prime numbers? It's because we found a proof of that fact: starting from the basics of math, we built out logical reasons for why there must be infinitely many primes. Proofs can be beautiful and elegant, but they also form the underpinning of math, and for students they're a great step to develop rigorous thinking and to work more like a mathematician.

How, then, can we ensure that students develop the skills to create their own proofs? This past summer, at our Summer Away site at Union College, BEAM piloted a new Introduction to Proofs course developed and taught by BEAM’s Learning and Pedagogy Manager, Javier Ronquillo Rivera.

“One of the main goals of the courses at BEAM Summer Away is getting students to start owning the process of proving things mathematically. This involves not only understanding the content that the class is covering, but also developing some habits of mind (and naming them) that mathematicians use every day. For example, looking at patterns, making conjectures from those patterns, trying to find counterexamples, or trying to find ways of being certain that the pattern always holds,” said Javier. “We decided to run this pilot to ensure that every student has the opportunity to develop the habits of mind and to have a common language around them.”

In the second half of the week-long class, Javier introduced the class to the MU puzzle, created by Douglas Hofstadter (and presented in Godel, Escher, Bach). The puzzle contains the letters M, I, and U, which can be combined to produce strings of letters. The solver is asked to start with the string MI and transform it into the string MU using one of four rules in each step. (Spoiler alert: the puzzle can’t be solved. The rules and more here.)

Javier explained, “By introducing this puzzle before developing the tools to prove its impossibility, there were two things I hoped the students would understand and feel: The first one is understanding the subtle difference between knowing that a result is impossible versus having tried many ways of getting to that result and not being able to. In the MU puzzle — without having completely developed the tools needed to prove the impossibility — we fall in the space of saying: ‘Is it really impossible to get the MU word, or have we just not found a way to get there by using the rules we have?’ I call the students’ attention to that uncertainty to show that in order to avoid that feeling, we need proof. The second thing I hoped students would feel, while using the tools we had at that time, is the need for mathematical proof.”

The puzzle stuck with Zayden, who wrote, “Although ‘MU’ is impossible, I built a connection that taught me to see patterns in these problems that I never saw before.” Andrew also reflected, “[I] worked on this for a while…it was very interesting because there are so many ways to try to come up with a solution.”

Led by Javier, students discussed their own definitions of arithmetic properties like even, odd, and divisible. Students explored how utilizing slightly different definitions led to different results, and collaborated to create strong definitions that required abstraction. For example, taking the definition “An even number is divisible by 2” and strengthening it to “An integer n is even if and only if n is twice some integer.” With these strong definitions, they were able to answer a variety of questions about different integers, included in the video below!

Visit Javier’s class [10 minutes].

BEAM Pathway students mentor a new cohort of mathematicians

BEAM students gave back in a big way this summer — 38 BEAM high school and college students served as near-peer counselors and teaching assistants at Discovery and Summer Away, mentoring BEAM middle schoolers while gaining valuable (paid) work experience.

For the first time, BEAM students also held leadership positions at all of our New York summer sites, serving as the Directors of Student Life (DoSL) across these programs. It’s a big job — DoSLs are responsible for coordinating activities, managing counselors, communicating with parents, and more. At Union College, the Guidance Counselor – who supports students in their social growth while at BEAM – and Associate Site Director were also BEAM alumni!

We’re incredibly proud to see BEAM students step up as role models for our newest cohort of students.

BEAM’s Learning and Evaluation team charts success!

The Learning & Evaluation Team at BEAM not only helps us demonstrate our impact, but also drives improvement across BEAM. Established two years ago, the team has brought new rigor to the evaluation of our work, which is, in turn, shaping how we design and implement our programs.

This summer for the first time, the L&E Team measured student growth in six areas that research has shown to be predictive of students’ future STEM success, and that are central to our work:

  • Math appreciation

  • Sense of community with BEAM

  • Growth mindset

  • Math-specific perseverance

  • Math self-efficacy

  • Math enjoyment

Students at both Summer Away and Discovery showed statistically significant growth in all six areas, with large effect size — which means we can attribute the effect to BEAM’s programs. (For all you nerds, we promised we’d get there, so thanks for hanging in.)

We’re incredibly excited by the strong results — and by everything our L&E Team is doing to make our work more effective.

For more information about BEAM’s 10 year vision for supporting our students’ STEM dreams, please read our strategic plan.

Quotable Quotes

We could write so much more about this summer, but our students say it best:

  • “BEAM wasn't just about math, I did learn new things but I was able to make connections with people and learn how some problems [have] a key to solve them.” -Lauren M, Los Angeles

  • “I grew a lot in BEAM. I think I became more independent and mature. I also made friends and the activities are fun.” - Desani M, New York City

  • “BEAM is a very interactive and rewarding program. It manages to make math feel like a sort of reward.” - Brian R, New York City

Jane Street and Hudson River Trading Summer STEM Scholars

We are immensely proud to announce the recipients of the Jane Street and Hudson River Trading Summer STEM Stipends, awarded to BEAM high school students in partnership with Jane Street Capital and Hudson River Trading.

At BEAM, we are working to make sure our students get access to the same sorts of STEM enrichment opportunities that their affluent peers already have, especially academic summer programs. To that end, BEAM provides individualized support in finding and applying to rigorous summer programs like Mathcamp, PROMYS, and more. This year, thanks to our corporate partners, we have been able to extend that support even further.

The Summer STEM Stipends are designed to address the fact that BEAM students who attend summer programs often cannot take summer jobs, which they and their families may be counting on. The stipends reduce the pressure of having to choose between getting paid for a summer job and participating in an intensive summer program. Attending such programs allows our students to explore diverse topics in STEM and prepares them for college and beyond.

Here is what BEAM students wrote last spring in advance of their summer STEM experiences.

Los Angeles 

Karla G - 11th grade - TeenArch Studios, UClA

I have been a part of BEAM since 2018, doing courses such as cryptography, topology, abstract expressions, and have worked with the Pathway Program as well as the BEAM Math Research Workshop. I enjoy learning more about fields of mathematics and the branches, doing programs on architecture and engineering during my spare time! I’m really interested in such things as the Artin braid group and the Torus knot, which I learned more about during my time at BEAM and reading books provided such as “Abstract Nonsense” and “Love and Math.”

Over the summer I am taking a course on Politics, Law, and Economics, at Yale University as a Yale Young Global Scholar. We’ll be learning about economic theories, government, and legal frameworks. This program will complement my activism centered on giving aid to marginalized communities and underprivileged areas. During the month of July, I will be taking a course at UCLA known as TeenArch Studios, a highly intensive, three-week architecture program, in which students work together to complete a project.

Daniel T - 11th grade - The Summer Science Program

Throughout my math journey up until 10th grade I viewed math as simply a subject I was good at that had very little applications to the real world. Then during my sophomore year I learned calculus and its applications in the field of physics. Then I really realized how interesting math can be. I became so hooked on calculus and physics that I wanted to learn a lot more than what was normally taught at school. I did this by taking higher level math courses such as calculus 3, linear algebra, and ordinary differential equations. BEAM also offered opportunities to learn math that was not normally taught in school which I was always fascinated by as well. After learning a lot of new things in these courses I am excited for what is to come in my math/science journey. This summer I am participating in the Summer Science Program at UNC Chapel Hill and will study astrophysics. I hope to learn about astronomy/space and how math and physics relate to it. Since I enjoy math and its applications in physics I know that I will enjoy everything that I will learn at this program. 

Alexis M - 11th grade - Canada/USA Mathcamp

I have been interested in STEM ever since the summer of 6th grade when I was first introduced to BEAM. The problems that we worked on at BEAM and the tight-knit community that existed was what hooked me. Alone, I probably wouldn't have grown as strong a passion for math. What excites me the most about STEM has to be the depth of many different topics, whether they are all math based or scattered throughout the sciences. For this reason, I continue studying STEM and hope to keep learning. The program I'm attending this summer is MathCamp, which I am returning to [after first attending last summer]. I hope to further advance my math skills and critical thinking.

Ashley V - 10th grade - Pomona College Academy for Youth Success 

"Falling down is a way for you to see another world, a world you have never seen before." This is a quote that stayed on my mind after hearing it, it felt so familiar. Now I realize, it felt so familiar because I had experienced it — with math. 

As I get older, math has become quite intimidating at times. I have fallen and fallen, over and over again. Failing to solve problems and spending hours of my day breaking my head over them, but there is something I cannot deny with every difficult math problem I have encountered: I always see something new. I always get to experience another world of math that expands my knowledge. So, if you ask me what has helped my interest in math grow, I would say I have fallen. I have fallen over and over again, and to be frank I can't wait to fall some more, if it means I get to keep exploring and discovering new worlds of math. This is my second summer attending PAYS. Last summer, the math class we took exposed us to math problems that truly challenged us.

Jacqueline O-V - 10th grade - Pomona College Academy for Youth Success

What most excites me about math is the many ways of coming to a single answer. At BEAM, I attended a Saturday class about stocks, which really piqued my interest in applying math to a job in the real world. This summer, I'll be attending PAYS, Pomona Academy for Youth Success, for the second time. Last summer at PAYS I discovered myself. I leaped out of my shell and made many close friends. I left behind timid me in Los Angeles and brought forward a confident me at Pomona. I made sure to participate every time I had an answer, right or wrong. I carried this confidence into all the other aspects of my life, including school. Going back to Pomona will give me the chance to, once again, discover new things about myself while still pursuing my education with the intense coursework provided.

Maya P - 11th grade - Turner-UCLA Allied Health Internship

I am what most people call a "STEM Nerd." I am proud of the title as my passion for STEM has driven me to discover new things about myself. The uncertainty that comes with learning something new within the STEM field is what really excites me and makes me want to continue pursuing STEM. I've attended BEAM and a club called MESA since 6th grade, and they have fostered and nurtured my love for STEM. 

This summer I will be part of the Turner-UCLA Allied Health Internship program which will further my knowledge of STEM careers I could pursue. I applied to the program because one day my mother was telling a story about a medical professional that worked at her job. Out of curiosity I asked my mother this person's job title and she said some hard to pronounce long technical name. I had never heard of the profession and looked it up. Upon investigation I realized I really knew nothing about what the medical field has to offer except for the typical doctor or nurse route. This internship is set to expose me to over 80+ medical professions that involve STEM and I hope that by the end of the internship I have gained a better understanding of the different career pathways within the medical field. 

Karen G - 10th grade - Scripps College Academy

I believe math and all fields in STEM have always been of my interest because of the career path that I want to pursue. I always knew I wanted my future career to be in the medical field but for a while I wasn't sure what position would best fit me. I decided becoming a delivery nurse would be ideal for me because you get to be part of welcoming life into the world which I think is a special moment to be able to be a part of. This summer I'm attending Scripps College Academy Program. During their summer program, I will be staying on Scripps’ campus for two weeks, analyzing topics in the real world that affect people's day to day lives.

New York City

Helen G - 11th grade - Summer High School Academic Program for Engineers, Columbia Engineering

I have been interested in math/STEM since I was in 3rd grade. My teachers really encouraged me to expand my knowledge. My 7th grade math teacher even took it a step further and helped me apply to BEAM, and I will always be grateful because to me STEM always has new things to learn about. I love problem solving and working with others, and that is what STEM is about.

Previously, I have done summer programs about different branches of engineering. In the future I see myself majoring in computer science but these programs helped me learn other potential fields I can major in. At SHAPE [Columbia Engineering's Summer High School Academic Program for Engineers], I hope to learn a lot more about computer science and also get to work with other students who share the same interests as me.

Yasong F - 10th grade - Lab Internship at Weill Cornell

Since sixth grade, BEAM has provided me with a lot of opportunities, resources, and support and has helped me develop a stronger interest in math. In elementary school and middle school, math class was always the class I looked forward to the most. I loved the way everything made sense and the satisfaction whenever I got a question right. It was during that time when I found out about BEAM. At BEAM Discovery, I met counselors and teachers who encouraged me to ask questions and made my questions feel welcomed. I also learned about math beyond the math taught in the school curriculum for the first time. 

I am interested in studying medicine. To become closer to my goal, I took AP Biology last year and I am taking a multi-year research course this year. Over the summer, I will be interning at a lab at Weill Cornell studying the effects of estrogen on blood pressure; I'm very excited to learn more about a subject I'm so interested in. Along with that, I will also be volunteering at a hospital.

Joelle N - 10th grade - Cooper Union Summer STEM Program

STEM excites me because STEM subjects are constantly evolving, with new theories, techniques, and discoveries emerging all the time. This means that there is always something new to learn, and the opportunity for growth and development are endless. The  logical reasoning and problem-solving abilities needed for mathematics and STEM topics are intellectually engaging and can help us solve complex challenges.

Both with BEAM and at school I was able to study math that addresses real world challenges. This summer I will be attending Cooper Union [Summer STEM Program] and based on my passions and interests I will create my own problems and projects that could have real world impact in the future. I hope to learn how to combine theoretical knowledge with practical skills while learning what the world needs through project management, project application, and teamwork.

Shreeya K - 10th grade - Science Research Mentoring Program, American Museum of Natural History

My STEM journey began as a child when I would always break things and rebuild them in an attempt to learn about how those things worked. Although I was a STEM enthusiast from a young age, I always found myself struggling in math as a child, primarily because I was new to the country and struggled to adapt to the new environment. However, when I entered the BEAM community during the summer of my 7th grade, it opened a whole new realm of math for me. I'll never forget that experience. I saw math with a new mindset and it completely changed the way I approached challenging math problems. Not only did I gain math skills, but I also learned how to apply those skills to other things such as finding the distance from sun to earth. I think seeing math in a new way unlike in school really helped me appreciate math even more and I will always thank BEAM for that. This summer, I'll be researching at the American Museum of Natural History with scientists in the astrophysics field to gain more experience in analyzing astro data. Through this program, I hope to gain hands-on experience working with astro data and improve my data analysis skills.

Lorraine A - 10th grade - Cooper Union Summer STEM Program

I am excited about the impact that STEM has. It makes things better and creates opportunities for a lot of people. I enjoy math because of the challenge; it also helps me improve my problem solving skills. Something that has helped my interest in STEM grow is learning about game development at The School of Interactive Arts. Although I don't want to work in game development in the future, I really enjoyed exploring it and learning coding. The program I am attending this summer is the Cooper Union Summer STEM Program.  I chose this program because I'm interested in learning about engineering and about Cooper Union. I hope to learn about the type of careers connected to engineering and if they fit with what I like to do.

Justin S - 11th grade - All Star Code

STEM subjects have real-world applications that shape the planet around us. They allow us to understand the complicated workings of the universe and develop practical solutions to address complex questions. Whether it's unraveling the questions of the universe, designing cutting-edge technology, or evolving life-saving cures, STEM fields have the ability to transform lives and create a positive impact on society. This potential to contribute to the advancement of information and better the quality of life for society globally is an important prospect that excites me about math and STEM.

Tasneem T - 10th grade - All Star Code

I liked dinosaurs growing up, it’s a weird fascination I've had since I can remember. One of my earliest memories is going to work with my mom and playing with a dinosaur figurine in the play area. I remember reading a lot of books about them too (I even cried when I found out they went extinct.) So since the age of 3, I've wanted to be a paleontologist.

That's what got me into STEM, simple curiosity and fascination led to something I see myself doing for the rest of my life. My interest has only grown since that time. [I chose to go to] All Star Code because it will give me tools that will help me succeed and give me an advantage in the future. There are many personal projects I have in store that require advanced computer skills like the ones I’ll be learning at All Star Code.

Ashfaq S - 10th grade - All Star Code

During 6th grade, I was opened up to the world of mathematics when my math teacher saw potential in some students in my class and introduced us to the math team and competitions and then, BEAM. This allowed me to explore my interests in STEM. Since 2020, participating in STEM programs has been hard, but I’m still interested in subjects like computer science and coding, which is why I chose to attend a coding program this summer. I hope to continue exploring computer science and hope that I can dive back into mathematics.

David L - 11th grade - All Star Code

When I joined BEAM, I got really interested in computer science. I remember going on repl.it and taking a python course. It expanded my creativity since there is no one right answer in python, you code to create your own world. In middle school, I had beginning coding classes and the usage of scratch and code.org. Then as I got to high school, I took a software engineering course where I learned HTML, CSS, and JavaScript. This summer, I'm attending All Star Code where I hope to learn more HTML, CSS, and JavaScript because I feel like there's more to learn.

Javier V - 9th grade - All Star Code

I first got introduced to BEAM by Ms. Perez, my 6th grade teacher. I was really into math, in fact, it was my favorite subject. I loved it even more when I got into 8th grade and took algebra with Mr. Joanis (I even got a 92 on my Regents exam). BEAM has given me the opportunity to express my natural passion for math and other related topics

I am attending a program in the summer called All Star Code. They teach people many different types of computer languages. You can also learn about different careers, such as game development, computer science, and much more. The reason I applied for the All Star Code program is because of coding’s connection to math. I love math so much because most of the time, there's one direct and definitive answer. Math also has many ways to affect the real world. When coding, I either input exactly what is needed and proceed with running the script successfully or unsuccessfully at which point I attempt to figure out the bug in the script. I wish to use all available resources to the full extent of my capabilities.

Kai G - 9th grade - All Star CODE

I first became interested in STEM around 5th grade. I was excited about how things fly, robots and technology, and how it could be applied. I started to explore STEM by going to various STEM camps, for example I went to a space camp during one of my spring breaks. When I went to BEAM, I got really curious about how I could solve different problems and the different ways to go about it! I chose to attend All Star Code this summer so I could learn about coding. I hope to learn how to make websites and how to make games. 

 

Mamadi K - 10th grade - Biorocket Research Internship Program

In STEM, I’m really excited about finance. I've taken classes in counting and statistics to help my interest in math/STEM grow. I'm attending the 2023 Biorocket Research Internship Program this summer because of the focus on science. I hope to learn about astronomy, human anatomy, microbiology, geology, neurobiology, and botany.

Kristen J - 10th grade - WorkForce 2000 Pre-RN Program

One thing that excites me most about math/STEM is how there are many ways to solve problems. I love how math involves a lot of critical thinking which allows you to explore the subject deeper and deeper so you can fully understand it. During my summer at BEAM Summer Away, I was given the opportunity to learn and explore different kinds of math. I saw how to logically think, different ways to work with fractions, and how to solve problems I would have never thought of. This opportunity led my interest in math to grow way more. The program I am attending this summer is a Pre-RN program. I chose this program because I would like to pursue a career in nursing in the future and I believe this program will help me learn more about it. I will use the math/STEM skills I have learned at BEAM and it will help me throughout my learning and research process as well.

Selina L - 10th grade - Brown Pre-CollegE

Math/STEM excites me because it allows me to use my hands and my brain at the same time. It also lets me have fun in the process. BEAM has helped grow my interest because during the summer of my 6th grade year, I was introduced to new kinds of math that I wouldn't be able to learn in school. This made me more interested in my math and science classes in school, making them my favorite. 

This summer I will be attending the Pre-college Program at Brown University and taking the materials engineering class. I chose this program because I get to explore one of my potential college majors, as well as experience college life and how it would feel being more independent, away from home. I decided to take materials engineering because I have always wanted to do some form of engineering, but I was never sure what. So this will help me learn if I would like to pursue materials engineering as a career. 

Selina Z - 11th Grade - Girls Who Code

Initially, I only liked math because I was good at it. But coming to BEAM, I realized that math isn't all formulas and unreasonable problems; it's actually fun. During BEAM Summer Away, I loved solving challenge problems and especially liked the sense of accomplishment when I finally solved it. BEAM allowed me to take classes outside of what was offered in my school and opened me up to new forms of math. BEAM has helped me foster my interest in STEM fields and made me want to pursue STEM not just because it pays me well but because I like it. This summer I'm attending Girls Who Code because I am interested in coding. I am excited to create fun projects!

Sylvan C - 10th Grade - STEM Institute City College of New York

I first became interested in math when my sister was preparing for the SHSAT [NYC Specialized High School entrance exam] and we reviewed the math questions together. In my first experiences with math, I was just given equations with operations that I had to evaluate to find an answer. I think too much of math is like this, where you are told what to do and how to do it and only asked to compute. I think it is much more interesting when a question is given without a set path to the solution. Finding how to solve something and why a solution works allows you to understand more and come up with new solutions rather than recycling formulas that you are just told to trust. My first experience at a math program was with BEAM Discovery. I took a class about patterns where we made formulas for patterns. This class is memorable to me because it represents the side of math that I love. We were asked to turn one mathematical concept into another. To represent observations using the language of math. 

This summer, I will be attending the STEM Institute at City College of New York. Last year I attended this program and took Precalculus as well as Chemistry. I would like to take these more advanced STEM courses in order to provide me with more scientific and mathematical background. The math that I am learning is fundamental to so many broader mathematical fields and concepts that I would like to understand.

Graduation Letter: Congratulations Zeñia!

Graduation season is an exciting time of year at BEAM, as the students we’ve known since middle school graduate and continue their incredible STEM journeys. This year, we introduce to you Zeñia Alarcon, who graduated from Worcester Polytechnic Institute this spring with a bachelor’s degree in mechanical engineering and a master’s degree in management. This month, she is beginning her career as an assistant superintendent with a construction management company. Congratulations, Zeñia!