**Cover Photo:***Zack L. ('15) created this year's cover photo, a clever edit of Packer's facade.*

## Historical and Current **Explanations**

**Algae Bio-Fuel**:*Sara V. H. ('16)**describes the advantages and disadvantages of algae as a bio-fuel and its place as an alternative form of energy.***An Energy Alternative:***The following, by Lucy M. ('16), was written in response to a Science Times article for her Advanced Chemistry class.***Clean Energy in Transportation:***This article by Zoe E. (’16) is an exploration of energy and climate change in the modern world, addressing how the world deals with these topics and specifically how transportation plays into climate change.***Calorie Restriction**:*The following submission by Lucas F. ('15) discusses calorie restriction and its affect on aging and lifespan.***Creating Energy in the Modern World**:*This article by Cecilia M. (’16) is an exploration of energy in the modern world. This includes the different tools that we use to get energy, how those tools work, and how we can implement them into our modern society with the different practical limitations that there are.***Dietary Intervention Impact on Gut Microbial Gene Richness**:*The following submission was written by Campbell P. (’14), and it summarizes an interesting article he read for his AP Biology class.***Earthly Applications for NASA Technology**:*T**he following was written by Eli C. ('14) and Maddy Y. ('14)***Explaining Relative Motion**:*This letter by Olivia F. (’20)***Exploring Artificial Intelligence**:*This article by William M. (’15) is an exploration of neurolinguistics and artificial intelligence, talking about how different types of artificial intelligence work and the effect it can have in the modern world and the issues present in this world. This article also talks about the study of neurolinguistics and how we can use this study to help fabricate artificial intelligence.***Gamma Function**:*This submission by Isaac E. ('14) is an article introducing and describing the gamma function.***How Leaves Work**:*This article by Nathan F. (’16) was inspired by an interesting Science Times article he read, and uses simple language to describe to complex process of how plants work.***Hydrogen Fuel Cells**:*The following submission by Jay G. ('16) was written for his Chemistry class and details the function and practicality of the hydrogen fuel cell as a source of energy for the modern world.***Music and Brain Development**:*The following submission was written by Cecilia M. ('16) for her chemistry class after a classmate asked a question on the topic which left her eager to learn more. It is a short research paper on the effect practicing an instrument has on children. It discusses the way it impacts children's brains as well as what scientists plan to do with this research.***Programming Calculators:***The following is a calculator programming tutorial written by Jack S. ('15) and Toby J. ('15).***The Science of Microsatellites**:*John F. ('16) wrote a short paper on the science of micro satellites, a topic he finds very interesting. During his research, he was surprised to find that the future of satellite technology is completely different from what he had thought before.***Sci-Fri Taser**:*The following submission by Lachlan M. (’15) was the final project for his symposium, Experimentum Crucis. He and his group were studying the connections between technologies shown in science-fiction, and their real life counterparts.***Sloane's Gap**:*The following submission by Emil H. ('15) explores a distribution of the integer sequences recorded on their website and the frequency with which they occur.***Sustainable Energy: Why Some Ideas Shine Brighter than Others:***This article by Joseph B. ('16) was for an extra credit assignment he had in chemistry. Joseph discusses the benefits and disadvantages of different types of sustainable energy.***Understanding the Galvanic Cell**:*The following submission by Belle F. ('15) explains how a galvanic cell works based on the galvanic cell that she constructed with Jordan K. ('15) as part of their Independent Study work.***The Virus: Our Unforeseen Philosopher's Stone:***This article by Jonathan D. (’15) is an exploration of viruses and their immense potential should we be able to understand and control them better. In this article, he talks about how they work, the different methods of study of these viruses, and examples of the different kinds of viruses that are “plaguing” us.***What Are Fuel Cells and How Do They Work?**:*After reading the New York Times article "The Artificial Leaf is Here Again," Sofia T. '16 became interested in fuel cells. She watched videos online and read articles from the head researcher of the project; her curiosity and research led her to write this article.*

## Mathematical and Scientific **Explorations**

**Astrocytes Expressing ALS-Linked Mutated SOD1 Release Factors Selectively Toxic to Motor Neurons**:*The following submission is Devon J. (’16)’s work on ALS for science research.***Big Bang:***For his final project for the Life's Big Questions symposium course, Will M. ('15) created a computer simulation of the Big Bang, which offers a possibly answer to the "big question" of how the universe was created.***Dictyostelium discoideum:***This submission by Raphael S. ('14) is a paper he wrote about the independent research he has been doing for the Science Research course offered at Packer. Raph has been researching how amoeba called Dictyostelium discoideum adhere to a flask as a model for cancer cell adhesion. He also included a copy of the poster he made based of his research that he used to compete in the New York City Science and Engineering Fair (NYCSEF).***The Future of Solar Cell Technology:***This submission by Giancarlo S. ('16) is a summary and explanation of the solar cells he has been studying called Intermediate Band Solar Cells (IBSC).**Being that he is in 10th grade, he has not yet worked with a mentor, nor conducted any research of his own, so this article is mainly based on bibliographic research he has done.***Guessing Through the SAT:***This article by Harmanpreet S. (’15) is an exploration of the SAT and the chances of the possible outcomes of randomly guessing every question on the SAT.***Hole Digging Using Geometry:***Three Lower School students, Sam, Sam, and Sophie, worked with teacher Christopher Natalie to solve a problem concerning the the volume of a cylinder, without ever having heard of pi or knowing the equation for the volume of a cylinder!***Make Your Own KenKen:***This piece by Maddy M. (’15) was done for Mr. Shah’s precalculus class. In this submission, Maddy describes how to create a KenKen Puzzle.***Measuring Boltzmann's Constant:***As a part of her Independent Science Research Course, Arielle C. ('14) worked at the Center of Soft Matter Physics department at NYU and was able to participate in an experiment using holographic video microscopy to calculate Boltzmann’s constant. Arielle and her fellow team-mates wrote an article summing up their findings, which was published in the American Journal of Physics in October of 2013.***Sum of All Natural Numbers:***The following is a proof reproduced by Tenieya H. ('15) in response to a New York Times article. The proof supplies the sum of all natural numbers. The article can be found here.***Summer at Sinai:***The following submission by Alex K. (’16) is a paragraph summary of the work she will be doing this summer for Science Research at Mt. Sinai.***What If?:***The following submission was written by Jack F. (’15) for his precalculus class; he investigates an interesting question that combines math with his love of baseball.*

**Reactions** and **Responses**

**Alternative Energy Sources, New but Unused:***In his response to a series of articles he read, George B. ('16), discusses the usefulness of new energy sources, but also why they have not been implemented in modern society.***An Insight Into the Curious World of Ethnobotany:***In the following article, Mitchell B. ('16) describes his introduction into the Ethnobotany field.***Challenging What We Think We Know:***This article by Eric M. (’14) is an explanation of part of Thomas Kuhn’s “The Structure of Scientific Revolution” that he was required to read for the Experimentum Crucis symposium.***The Current State of American Education System:***In his piece, Jackson C. ('15) responds to an article written in the New York Times and critiques the American school system. He compares his unique experience at an elite private school to that of the majority of American students, who attend public school. The article he is responding to can be found here.***Discovering New Numbers:***This article by Alex S. (’16) is an assignment she was given in Mr. Shah’s precalculus class in which students had to explore an interesting aspect of math. Alex’s submission discusses some of the things she found interesting in a Times article she read about humans discovering numbers that previously seemed impossible. The Times article can be read here.***Interview With an Architect:***The following interview was conducted over the phone by Jed R. ('15) on February 16, 2014 for his precalculus class.***Life of Pi Response:***A Packer student studying Advanced Pre-calculus read and wrote a response to a New York Times article which discussed the existence of infinity. The original article can be viewed here.***Mathematical Art Video Commentary:***In her submission, Michaela D. ('15) comments on a video about the famous “mathematical” artist M.C. Escher, notorious for his work with perception, patterns, and optical allusions .***Missing from Science Class:***In her response to a New York Times article, Maddie S. '15 discusses her opinions on the disparity of both women and minorities in tech-oriented fields. The article she is responding to can be read here.***The Museum of Math:***The following submission was written by Gabriel W. (’15) for his precalculus class. It’s something relevant to all math and science students, a review of America’s first museum of math, MoMath.***The Inside Scoop on a Real Mathematician:***This interview by Michael W. (’15) is a closer look into the life of a mathematician and the reasons why they love math, their specific studies, how they apply math to other parts of life, and how their studies might connect to high school math.*

## Artistic **Creations**

**Art Using the Fibonacci Sequence:***The following work was created by by Alex J. ('15) for her pre-calculus class. She explored art on a checker-styled board where she used the Fibonacci sequence to determine the size of each of the boxes.***Computer Generated Architecture and Designs:***These images by Jack F. (’15) are a compilation of computer generated designs for various structures that Jack enjoys making in his free time.***Mathematical Landscape:***This article, by**Jordan K. ('15)**was written**for Mr. Kinnell's Math Art symposium describing the mathematics behind a piece of artwork he created during the course. He dubs the resulting math-art "marth."***Math Art:***The following "math art" was created by**Giovanna A. ('15)*f*or her pre-calculus class. She made the three symmetrical designs using a computer program called Silk.***Math in Music:***This submission is a piece from Lily C. ('15) that she did for her Precalculus class. She wrote about writing sine graph equations for different musical pitches, and how math was used in the development of different tuning systems in music.*