Table Of Contents

  1. Cover photograph for the inuagural issue of Intersections
    This cover photo, taken and edited by Mac S. (’13), was commissioned by the editors of Intersections. After brainstorming what we wanted the cover to represent, we decided a simple crossroads of math and science, made literal, would perfectly fit the bill. The photograph, taken by Mac, is a quintessential Brooklyn image, taken a short walk from our school in DUMBO. If you look closely, the photographer has not only digitally changed the street signs, but there is some math digital math-science graffiti added to the green box below the street signs.

    Historical and Current Explanations

  2. B-text
    This submission by Michaela D. (’15), Chloe-Kate A. (’15), Toby J. (’15), and Tenieya H. (’15) is from a project they did for their tenth grade history class.
  3. Costa Rican Adventure
    The following piece by Belle F. (’15) and Jack S. (’15) is about the Packer Spring Break trip to Costa Rica. It includes a summary of some of the information the participants learned about sea turtles, as well as what they did on the trip and their take away from the experience.
  4. Electing Math President of the Universe and Other Fun Stuff
    In Ms. Danforth’s Advanced Math Applications class first semester, her class researched all aspects of elections and apportioning representatives to the states for the House of Representatives.  Some people researched voting methods, some researched apportionment, and some researched the Electoral College. In the end, they created PowerPoints of the main ideas of each area.
  5. How Space Shuttles Work
    The following is a research paper, written by Nathaniel H. (’14) for Mr. Ruch’s Astronomy and Geophysics class. This research paper explains how a space shuttle works.
  6. Pharmaceutical Companies These Days
    The following is an essay written by Oakley F. (’13) for Dr. Lurain’s Organic Chemistry class on the subject of pharmaceutical companies. 
  7. The Poetry of Mathematics
    The following is a Brooklyn Female Academy paper from January 1853–it talks about the fire that burnt down the school and that eventually led to Harriet Packer funding the school.  That said, in there, there’s an article (see top, 2nd column) about the mathematics of poetry. Dr. Strauss kindly provides analysis for this article.
  8. Polling Down Capitol Hill
    This is a research paper by Keegan M. (’13) describing the history and origins of public opinion polling with a particular focus on the 1936 US presidential election.
  9. Uncle Sam, Protect us from Trans-Fats
    The following is an essay written by Oakley F. (’13) for Dr. Lurain’s Organic Chemistry class on the subject of health with regard to trans-fats.
  10. What’s Hurting Our Ozone Layer: CFC for Yourself
    The following is an essay written by Oakley F. (’13) for Dr. Lurain’s Organic Chemistry class on the subject of chloroflurocarbons harming the Earth’s ozone.

    Mathematic and Scientific Explorations

  11. A Challenging Chalkboard Problem
    This article, written by Alex S. (’16), poses an interesting puzzle-like problem that you can play around with when you’re bored on the subway. It involves just one simple process, but leads to a really involved answer. Alex comes up with a possible solution to the problem, but then proves the solution true using a process called mathematical induction. She ends by leaving the reader with some interesting (unanswered) questions that this problem brings up.
  12. A Permutation That’s Far From Abstemious
    This article, written by Ellie F. (’14), provides an in depth explanation on how to find the number of permutations of a word with a unique property.
  13. Brownian Motion
    This is a summary of the work that Arielle C. (’14) is doing at a lab at NYU for science research. It includes some of the articles that she has read, as well as the type of work that she is doing. This was written in preparation for the Science Symposium in May. The artwork below was also done by Arielle for the Science Research Symposium’s invitation.
  14. Cell Research
    This is a research summary Raph S. (’14) did for the science research class he is in at Packer. He compiled a summary of all the work he has done so far and data he has collected in the lab to date. This summary includes his own data that he collected once every week for an amoeba named dictyostelium discoideum.
  15. Curious George
    This submission from George T. (’15) is simply a mathematical question that interested him when he was in fifth grade. After pondering it over, he realized that there was a trick to solving it. The question is a little like a brainteaser.
  16. DIY: Center of a Circle
    The problem that John B. (’15) submitted is a challenge problem from his math class, which was to find the center of a circle using a sheet of paper and a pencil. Knowing that the intersection of the two diagonals of a rectangle inscribed in a circle is the circles center, he used the edge of his paper and the corner to make an inscribed rectangle in the circle.
  17. Math Club Cryptography Problem
    Will M. (’15)’s submission is a computer program, which he created to solve a problem  presented by the Math Club. In addition to the source code, he wrote a short explanation and made some graphics which should help explain his solution. The explanation talks about the process he went through while making the program and  how small optimizations that he made to the code dramatically decreased the program’s execution  time.

    Artistic Creations

  18. An Art Problem
    Cameron D. (’14) created a piece of art that illustrates the INTERSECTION of the world of art and the world of math.  He wanted to demonstrate visually the confluence of his interests and how things can be looked at from a variety of perspectives.  Specifically, his illustration is of the typical sphere most art students draw in order to practice skills such as shading and perspective with the only addition being the formula for volume in the background.
  19. A Little Poetry
    The following are two poems by Claire R. (’13) about humans’ role in global warming and maltreatment of the Earth.  The first poem she wrote for her Bible as Literature class, and the second one she wrote on her own.
  20. Counting Art
    The following mosaic was created by the first grade students of Ms. Copland. They were inspired by Alighiero Boetti’s artwork.  They show pictures of the process of making their mosaic and provide a link to a VoiceThread, where they explain more specifically what they did and why their artwork is secretly very mathematical.
  21. Family of Curves
    This is a math project that Arielle C. (’14)’s class did during SAIL week. The project was to create a cool looking graph using only one equation and then to describe what they liked about their graphs, what they wondered, what they noticed, and what the transformations were. They created “booklets” of their graphs and included five small graphs of different curves in their “family of curves”.
  22. GeoGebrawesome
    In Mr. Shah’s math class last February, Ali K. (’14) had a project in which she had to come up with a general equation to make a family of curves, which features variables to make different values for each equation. For her equation, her values were between -5 and 5. She graphed her equation into an amazing program on the computer called GeoGebra. She played around with the window and zoom, so the piece could look as best as possible. She thought this project was a lot of fun because it was great to see that mathematical equations can create actual artwork. She also discovered that coming up with the most convoluted equation does not mean the piece will be cool looking.
  23. Luck Be a Lady Liberty
    Jonathan D. (’15), a self-proclaimed Rubik’s Cube geek, competes in competitions throughout the United States and can solve a cube in less than twenty seconds!  He began creating mosaics out of Rubik’s Cubes in ninth grade to generate interest in his club.  Below is a mosaic of the Statue of Liberty that he made out of 225 Rubik’s Cubes.
  24. Matharchitecture
    This series of pictures, composed by Jack F. (’15) using Google SketchUp, includes designs of structures using common geometric shapes.  Jack enjoys making these designs in his spare time.  Included before each picture is a description of the design.
  25. Strong Familial Curves
    The following is a submission by Nick S. (’14) that he did for a pre-calculus project.
  26. The Art of GeoGebra Sequences
    Allison R. (’14) completed the following project for Mr. Shah’s pre-calculus class.
  27. The Very Model of a Modern Natural Satellite
    Hope J. (’13) wrote a song naming all of the natural satellites (moons) in our solar system.  The song is based off of Tom Lehrer’s, The Elements Song.

    Classroom Continuations

  28. 3-D Graphing
    This year’s Multivariable Calculus class, consisting of Brynna D., Peter H., Sarah J., Keegan M., Jake S., and Mac S. all of the class of ’13, spent a lot of time thinking about 3-D graphs, partly because it was required of them to understand multivariable calculus and partly because they were curious about how to fully understand it.  At one point they did a project to make their own 3-D graphs from notecard graph printouts.  The following is an explanation of how they came to understand 3-D graphs, how to make your own, and some applications to real life.
  29. A Review of a Science Youtube Channel
    This is a review by Andrew R. (’14) of a YouTube channel that he refers to as “really cool.”
  30. Running in Circles
    Egan M. (’14) describes the equation of a circle and how that relates to the equation of a sphere. He wanted to show how the equation of a sphere can graph a 3 Dimensional object. He does this by starting with things we know (namely circles) and understand in two dimensions and then generalizes these things into the third dimension. He also plays around with circles in two dimensions and comes up with the notion of an ellipse, and then generalizes that ellipse into the third dimension. Finally, he shows us by tinkering around with the equation of the objects he’s created in the third dimension, he can generate some amazingly beautiful three-dimension graphs which merit further exploration.
  31. The Science of Black Holes
    Branden L. (’13) wrote a small report on the science behind black holes. As the final assignment for the Astronomy unit in Mr. Ruch’s Astronomy and Geophysics course, students were tasked with researching topics in astronomy. He was curious about black holes, so he took to the internet to research it and wrote about what he found. He also provides the reader with a link to read more about black holes here.
  32. Touching Base With Chem Club
    Mark S. (’15) submitted a video about Packer’s Chem Club, showing some of the cool experiments and fun times that they have. It gives a taste of the club’s awesomeness, and hopefully those who see the video will come out to Chem Club. He did this because he had been filming a number of the club’s experiments over the past year, and he thought that it would be cool to put together his videos into something that can inspire others to take an interest in chemistry. So, he gathered his videos, put them together in this short, promo fashion, added some music, and he had his video. He urges people to “Come out to Chem Club!”
  33. Transcendent Fractals
    Jasen C. (’15) wrote a computer program for his tenth grade English class’s transcendental project where he constructs his own fractal while playing the Chaos Game.