Recall that the problem statement of my project is to quickly and autonomously navigate and map a burning building, identify trapped inhabitants, and send recovery/escape routes to firefighters as fast as possible. During my background investigation of this subject, I discovered that navigating fires has traditionally posed a challenge for robotic systems. Traditional LiDAR (Light based) sensors are often employed for SLAM (Simultaneous Localization and Mapping: A class of perception and mapping algorithms), but these sensors lose accuracy significantly in smoke. Meanwhile, SONAR (Soundwave-based) or RADAR (Radio-based) mapping systems are often very bulky and technically complex, making them challenging to incorporate onto a dynamic robotic system. This posed a perception challenge: to develop a novel perception and navigation system that can function effectively in a fire environment.

In fifth grade, I joined a FIRST Lego League robotics team, and although my team of all first-years placed dead-last at our first ever competition, I was completely hooked. This was the beginning of my obsession with robotics. I would go on to do 8 years of FIRST robotics, through 12th grade … Having seen my programmer-teammates code elaborate autonomous routines and automations for the robots I designed, I naturally became curious about the software that controlled the robots as well. As the Covid-19 pandemic lockdown began, with some more time on my hands, I set a goal to explore this new realm … At the same time, I heard about new trends in robotics–autonomous machines that could disinfect facilities with little to no human involvement, robotic nurses to deliver supplies and materials to the sick, robotic emergency responders, and more. I learned about the tremendous potential of autonomous mobile robots in service applications … This was plenty enough motivation for me to get started. I borrowed one of my robotics team’s old robots and got to work in my garage, starting with YouTube tutorials and learning the basics of motion control. I didn’t quite know what I was researching yet or what my end goal was, just that I wanted to become an expert in this field and build something useful and novel; the rest I would figure out later …

From the time I picked up Basher Science’s Physics: Why Matter Matters! in third grade, understanding how the most fundamental physical processes create the reality of our universe has wholly fascinated me. The ability to mathematically and scientifically explain why something happens, from a single subatomic interaction to the inescapable pull of a black hole, is what drew me to the field of physics. My exploration took the form of documentaries, MinutePhysics videos on YouTube, books, and, when I entered high school, classes that allowed me to develop my understanding of the field in a more comprehensive way. When I was accepted to a summer research program for high schoolers at the Laboratory for Laser Energetics, I was excited to finally apply my learning experiences toward real-world scientific inquiry and solving novel problems … The Laboratory for Laser Energetics (LLE) at the University of Rochester is dedicated to the study of high-energy-density physics. During the eight weeks I spent there, I worked with a senior scientist at the lab, Dr. Stephen Craxton, and was given a project to pursue. Initially, my project was centered on using 2D hydrodynamics computer simulations to optimize a cone-in-shell target intended for backlighting opacity experiments at the National Ignition Facility. The double cone-in-shell target was first proposed by Dr. Robert Heeter of Lawrence Livermore National Laboratory (LLNL) in order to achieve a short-pulse, point source x-ray signal, which was ideal for backlighting the opacity samples that scientists at LLNL were investigating. Eventually, my work expanded to developing an x-ray diagnostic code that could predict emission histories for the various targets I had simulated. By the end of the program, I had developed an optimized design for a double cone-in-shell x-ray backlighter through analysis of both simulation output data and calculations performed by the program I had written. Through the course of my time at LLE, I found myself not only applying what I had learned in my calculus, physics, and computer science classes, but also discovering new concepts that enabled me to achieve the goal of my project. For example, my advisor assigned me a variety of reading materials at the start of the program, including former high school students’ project reports as well as published papers. I also had to become familiar with the mathematical model - the radiation transfer equation - that would be central to my x-ray diagnostic program. My prior coursework in calculus allowed me to better understand the equations and derivations relevant to my project. I also had to learn Fortran as that was the programming language I developed my code in. I found these learning experiences to be enriching and exciting, as I was implementing my new knowledge to address a real and relevant problem in the field of physics…

Last year, the researcher outlined the mathematical basis of a new quantum secure direct communication (QSDC) protocol. QSDC protocols are methods of information transfer which gain security from the use of quantum mechanical effects. Due to the measurement principle, quantum communication reveals eavesdroppers with a probability arbitrarily near unity. In a world where traditional encryption is increasingly threatened by quantum computers and Shor’s Algorithm, QSDC protocols provide impregnable security to banking transfers, diplomatic wires, and general communications. In contrast to existing QSDC protocols, the researcher’s protocol does not require the use of entanglement, which can be technically difficult to create and maintain without succumbing to decoherence and collapse. Further, the researcher’s protocol can be implemented with simple optical elements, transmits information directly, and retains quantum security advantages … Recently, IBM allowed the researcher to run trials on a real quantum computer, with a success rate above 90%. Given the promising results of the project, the protocol may soon be used to protect businesses, governments, and private citizens from certain types of monitoring, espionage, and cybercrime.

A recently emerging and novel method of the observation of galaxies is through Integral Field Unit (IFU) Spectroscopy. Spectroscopy - in contrast to photometry which measures the total brightness or flux of light - allows us to see the amount of light observed at each discrete wavelength within the observed range. Accordingly, since many physical processes are associated with the absorption or emission of light at specific wavelengths, we are able to measure these processes in distant objects through spectroscopy … In this work, I seek to apply some of the unique forms of analysis permitted by IFU spectroscopy to the phenomena of dwarf interactions. One such innovation which IFU spectroscopy allows for is the examination of 2-dimensional resolved velocity dispersions, maps which display the movements of discrete stellars and gaseous elements within the galaxy.

The future of science and technology lies in the quantum properties of matter, with fields such as condensed matter physics having already produced innovation like nanotechnology and quantum computation. Superconductivity, the property of some materials to show no electrical resistance at extremely low temperatures, and magnetic exchange coupling, the interaction of ferromagnetic materials over space, have in past research shown tendencies to interact with one another in interesting ways. Should that relationship be better understood, it would enable us to utilize them to improve practical applications of technologies such as maglev trains. Our project investigated these dual phenomena, asking how the two are related, so that we might gain a better understanding to how and why they interact, possibly yielding insight to future applications of their relationship.

Previous studies have shown that the cosmic expansion is accelerating despite the gravitational attraction between matter, caused by a mysterious source of energy denoted as dark energy. A cosmographic test of whether it exists in the form of a cosmological constant or more general dark energy was performed with Markov chain Monte Carlo algorithms using the SCP Union2.1 supernova compilation. By fitting polynomials to Hubble series expansions, the Hubble Constant (H0), the deceleration parameter (q0), and the jerk parameter (j0) can be estimated … This study focuses on the effects of MCMC algorithms and model-building uncertainty the dependence of results based on fitting functions used. Eight tests of different orders and distance scales were performed. Through a new program devised in Java, resulting uncertainties of all parameters are significantly smaller than those from traditional statistical techniques. Combined with cosmographic method, MCMC yields much more Gaussian distributions of cosmological parameters.

Then finally, after several years of messing around in the theoretical space inside my head, I came across a specific topic where further research could be of legitimate use: space based solar power (SBSP). SBSP is exactly what it sounds like: solar power but in spaaace! Large solar panels are launched into orbit, specifically geosynchronous Earth orbit, and beam collected energy, via microwaves, back down to Earth for use. It’s clean and efficient; considering the existential threat of climate change, it’s exactly the kind of energy source we need. I was just in my room, on my computer, moseying around the internet, when I came across the wiki page for SBSP; the first thought that went through my head was, well, no duh! This is brilliant! Why hasn’t this been implemented yet?! The second thought was, why is my internet so slow?! And the third thought was, whelp, I need a book now.

My advice to high school students looking to work on a research project that combines science and mathematics is to be invested in learning a lot of new things and keep an open mind as high schoolers, there’s a lot of mathematics we are unfamiliar with, and sometimes it’s easy to get overwhelmed. However, I would say that the beauty of combined science and math research is that you learn so much about mathematical theory that can be applied to the science a double-pronged approach, if you will! It’s a fantastic opportunity, and with an open mind and willingness to learn it becomes that much better and more rewarding … This research describes how a concentrically embedded bubble alters the surface wave of a suspended viscous drop. The analysis considers small amplitudes of the interfacial pulsation so that the nonlinear convective terms can be neglected in the flow equation. The consequent linearized system is represented by a matrix formulation which predicts the natural frequencies and decay constants for different modes of oscillation. The involved matrices have a block diagonal structure separating the deformational and rotational groups. The presented work includes the mathematical derivations for both groups proving that the former manifests both oscillating and decaying features while the latter only exhibits monotonic decrease. The results reveal the variation in decay constants with bubble-drop size-ratio for different rotational modes …

One of the great remaining mysteries of modern physics is the accelerating expansion of the universe. It has been proposed that dark energy is responsible for this phenomenon. In order to understand dark energy, it is necessary to compute the energy density of the vacuum that arises from the fundamental theories that describe the universe. The vacuum energy density appears in Einstein’s theory of general relativity as the famous cosmological constant, and was first introduced in order to establish a static universe. General relativity would have otherwise predicted an expanding or contracting universe, and it was generally believed at the time that the universe was not changing in size. Later, when Hubble discovered that the universe was indeed expanding, Einstein discarded the constant. However, there is nothing in general relativity that forbids the introduction of the cosmological constant, and today, it is clear that its value must be found if one is to use general relativity to explain dark energy.

My project originated long ago, when I was barely an infant. Almost every day I visited the Museum of Natural History and had lunch underneath the blue whale after touring the museum, paying special attention to the dinosaurs. Ever since I was young, dinosaurs have held that special interest for me, not in the sense of big scary monsters of a world long gone, but more in the sense of marvels of nature, amazing creatures at the zenith of evolution … when the time came to design my research project, I knew there was only one choice. I had to try and find out how dinosaurs moved …

It wasn’t until my sophomore year in high school, however, that I became interested in astronomy. I had heard from other students at my school about the Science Internship Program, which gives research opportunities to high school students and is run by UC Santa Cruz Astronomy and Astrophysics Professor Raja GuhaThakurta. I discussed possible projects with Raja, who became my mentor, and ultimately decided on my project, a search for very distant galaxies, because I thought it would be exciting to look back in time. I continued my research for two years, completing most of it over two summers at UC Santa Cruz. During the first summer, my project focused on manual search, which was exciting because I discovered several new Lyman Alpha Emitters, the type of galaxy I was looking for. However, this process of manual search was quite time-consuming, so when I came back the next summer, I combined the project with my passion for efficiency and computer science and worked on an automated search algorithm … The goal of this project is to look back in time to observe objects in the early stages of the history of the universe. Astronomers can observe what occurred billions of years ago by looking out into the distant universe. The farther away an object is, the farther back in time we are observing, because the light emitted from objects takes more time to travel to us. Thus observing objects that are very distant is essentially looking back in time.

I’ve lived in the small town of Burnt Hills, New York for all of my life. Starting at a young age I developed a love for science. In my spare time I would polish rocks in my rock tumbler. I spent hours digging around my gravel driveway trying to pick out the quartz among the limestone. I also enjoyed analyzing fingerprints with my toy forensic kit. At one point I actually wanted to become a forensic anthropologist (the show Bones was a favorite of mine). My father had a part in helping to propel my scientific interests. He had an old chemistry set and we would do experiments on the weekends. He also would set up his old telescope so we could gaze at the stars. Perhaps that’s where my love of astronomy began. My interest in nature also influenced my passion for science. As a little girl I would catch frogs, butterflies, crickets - really anything I could get my hands on. I loved, and still love, fishing at my grandparent’s lake, only a couple hours from where I live. Bloody Pond, despite the gruesome name, is where I have had some of my best memories. I’ve especially enjoyed my time spent looking up at the sky on those clear nights … As I got older I watched documentaries and read books on concepts like light speed and parallel universes, which immediately captured my imagination. I was in awe by how the world works and how we can learn about it through equations and experiments. What drew me to astronomy and physics is the idea that it is the basis of study for the entire universe; from the most elementary of particles, such as neutrinos, up to the largest and most distant galaxy structures studied. My passion for science was escalated the summer going into my sophomore year of high school. That summer I attended a career exploration program at Cornell University where I took a workshop on astronomy. Immediately I fell in love with the field and the exciting research it was producing. I was fascinated by dark matter, exoplanets, and all of the mysteries in the farthest depths of our universe.

The title of my paper was “The Sky’s the Limit- An Investigation of Cloud Cover on Major League Baseball Performance.” My research project was inspired by a genuine passion for the game of baseball and my desire to learn more about its subtle nuances. I often wondered how much weather variables such as sun, clouds and shadows affected the outcome of a game or individual player performance. My curiosity prompted me to do some preliminary research to identify whether these questions were previously investigated. This served as the impetus for my project and interestingly the results only led me to formulate more questions … The focus of my project was to investigate whether different percentages of cloud cover during a baseball game favored batters or pitchers. Additionally, what effect cloud cover percentages had on fielders during a Major League Baseball game? The data collected for this investigation was obtained from the years 2007 to 2010. Baseball data gathered during day conditions were also compared to baseball data gathered during night conditions to see if any significant differences existed. Baseball data was collected from www.baseball-reference.com and weather data was gathered from the National Climatic Data Center. Seven variables were compared across three categories of cloud cover, 0-29%, 30-79% and 80-100% cloud cover during day games and night games, which served as the control for my study. The overall results suggest that clearer conditions tend to favor the pitcher in each day game while cloudier day games tend to favor the batter.

Imagine being plunged perpetually into a silence where the ubiquity of sound is irrelevant. That is the world which many students in my high school experience. My inspiration for this project really came from the students in my high school’s Deaf and Hard of Hearing (DHH) program. My school has a department which offers a high school education to DHH students across Orange County. The students in this program take many of the same classes as the other students, using an interpreter to understand the lectures. I befriended several DHH students, but one in particular stood out to me: a boy in Cross Country who was deaf but used a device called the cochlear implant to hear. During the team’s annual trip to Yosemite each summer, he picked a song on a friend’s MP3 player and played it. He then told the group that the song he chose was his favorite song. This moment inspired me, as it showed me that even deaf individuals could find enjoyment from music. As a pianist for 12 years, I felt an urge to help him and other DHH students fully experience the wonders of music … So let me give a bit of background information on the cochlear implant. The cochlear implant bypasses the outer, middle, and inner ear by sending electrical stimulation directly up the auditory nerve to the temporal lobes of the brain. This electrical stimulation mimics the natural electrical signals produced by the hair cells in the cochlea, and the implant users are able to interpret this as sound. Because it completely bypasses the ear, this device enables otherwise deaf or critically hard of hearing individuals to hear.

Ever since Galactic Cosmic Rays were detected by Victor Hess 100 years ago (Hess 1912), their origin has been a mystery; what stellar object is powerful enough to accelerate particles into TeV energy ranges, and how does it release so much of them? Galactic Cosmic Rays are capable of releasing high energy X-rays and gamma rays, with energies up to GeV, as they travel through the interstellar medium. By studying the spectral patterns of the emitted X-rays and gamma rays, we can gain insight into the nature of the Cosmic rays themselves. To record such patterns, astronomers have used the Chandra telescope and the Very Large Array telescope to create high-resolution X-ray images of some sources of Cosmic rays. However, the low energy band of these preexisting telescopes has limited our ability to detect high-energy X-ray emissions from the sources and to gain further understanding of their particle acceleration mechanisms (Reynolds 2008). But with the recently launched Nuclear Spectroscopic Telescope Array (NuSTAR), it is now possible to record these high-energy spectrum data with high resolution.

My inspiration came at breakfast one day, when CNN switched to a story about the Icelandic volcanic eruption that had grounded air traffic across Europe (due to the abrasive, potentially explosion-causing action that debris has in engines). My immediate thought was, “Someone should fix that.” … I always am asked whether foreign object damage, FOD, is really that major a problem, because most people have seen a few news reports on jets crash-landing after bird strikes or other major accidents, but they don’t know that thousands of these incidents, albeit more minor, happen yearly. Not only by number, but by cost, it clearly is a major problem in aviation. Boeing estimates a minimum yearly cost, barring any disasters like the 1.7 billion dollar Icelandic volcanic eruption, of at least 4 billion dollars a year from FOD.

Despite my enthusiasm for science, I was initially nervous about conducting research, and I was hesitant to apply for the Research Science Institute. I had always assumed that meaningful research was in the domain of Ph.D. professors and graduate students, far outside the reach of high school students like me. Given the complexity and dangers of nuclear energy, I thought that this would be especially true for the area in which I was assigned to work. However, while a professor’s research in general can be highly complex, there are often parts with which high school students can assist. Research certainly poses challenges and can be difficult, but I advise that you do not discount it simply due to lack of experience . . . Compared to fossil fuel-powered plants, nuclear reactors can extract a tremendous amount of energy from fuel through a process known as nuclear fission. A conventional nuclear reactor can provide roughly 360,000 kilowatt-hours of electricity per kilogram of uranium used; in comparison, coal-fired plants generate about 3 kilowatt-hours per kilogram of fuel. However, an even larger amount of energy remains unused, as conventional nuclear reactors only use about 5% of their fuel (1). The remainder of the fuel along with radioactive products of fission � is disposed of as nuclear waste .

Physarum polycephalum is an organism that one cannot help but find interesting. This single-celled amoeboid is able to self-organize and self-optimize without the help of any sort of central nervous system. It can find the shortest path connecting any number of food sources, solve mazes created by physical barriers, and create paths that avoid light. I was introduced to this organism by my mentor, a member of the Laboratory of Mathematical Physics at The Rockefeller University in Manhattan, New York. The general theme that connected the research within this laboratory was optimized networks; researchers worked on everything from the venation in plant leaves to the structure of rat brains. There was no work being done with Physarum polycephalum at the time, but my mentor cited its venation patterns as examples of optimized network . . . I began to wonder if I could take these [existing] mathematical models a step further by creating a computer program that could model the organism’s behavior continuously rather than discretely. This would not only provide useful insight into the optimization process itself, but would also be an educational exercise in creating a dynamic simulation from a static model . . . Perhaps the most valuable lesson I learned from conducting research throughout high school is the importance of stupidity. This phrase, borrowed from the title of an essay by Martin Schwartz, means that before you can focus on discovering, you have to free yourself from the burden of knowing. You will almost inevitably encounter roadblocks throughout the research process, and it is important not to let the feeling of stupidity discourage you from continuing. The truth is comforting: when one is conducting research, he or she is not expected to have the answers. We enter the unknown in the pursuit of knowledge, and what we discover brings us closer to understanding.

My interest in physics was born rather serendipitously in middle school when I stumbled upon the popular physics section of my local library. In no time at all, I told you the qualitative details of Young’s double slit experiment and how it contradicted certain previous classical notions of physics, but I could not have have taken a simple integral to save my life. So, due mostly to my lack of mathematical sophistication, I didn’t do much physics until my junior year of high school. At that point, I realized that I could actually just go to the library, check out books, and learn math and physics on my own, which is exactly what I did. Although all of this self-learning was undoubtedly valuable, the one experience that was truly integral to reinforcing my interest in math and physics was the research project I conducted (and eventually submitted to both the Siemens and the Intel STS competitions) in the summer after my junior year . . . I conducted the research at the University of Maryland, in the Theoretical Quarks, Hadrons, and Nuclei group (TQHN). Naturally, I was really excited to be working on real problems in theoretical physics - problems I had previously only read about. My research, which I will discuss below, focused on Quantum Chromodynamics, which is a part of the Standard Model of particle physics that deals with quarks and their interactions . .

Pragmatically, the inspiration for this project is drawn from a series of backpacking excursion I embarked upon with my brother and father two years ago, which in the end totaled approximately 120 miles. Now the golden maxim of backpacking is to pack frugally. So, every day as I repacked my backpack, I would glare angrily at the extra weight of fire by friction set material I had to carry with me because it made the overall weight of my bag very onerous. Then, as I trudged along the trails throughout the day, I started to mull over the idea of possibly constructing the optimal fire by friction set. The more and more I thought about it the more and more that I wanted to find the answer to this curious concept. Subsequently, when my junior year started, I decided that I had to investigate this query of mine, so immediately started doing some background research.

Looking up at night, it is easy to get lost in the grandeur of the view. Space seems infinite and the myriad stars inspire a multitude of feelings. Ever since I can remember, I wanted to understand the great mysteries of the universe first getting excited via buzz words like “black holes” and “curved space time.” Such fascinating ideas easily captivated my childhood curiosity . . . My interest started to become more tangible in elementary school when the school’s librarian recommended me to read Stepehen Hawking’s “A Brief History of Time.” With the help of my father I finished the book and became noticeably more interested in astrophysics. I began dreaming of becoming a research scientist much like Einstein and discovering how the universe “works.” . . . My research project looked at a mathematical function called the two-point correlation function and applied it to measure the clustering of galaxies in a radio survey of the sky. This is important because it was the first time such an analysis was done in a frequency relevant to a new area of astrophysics called 21 cm tomography which hopes to give us precise measurements of cosmological parameters and insight into the very early universe…

From the very beginning of civilization, humans have pondered their future through innumerable myths and legends. Through the times of the ancient Greeks’ tales, with their stories of oracles prophesying the ruin of empires, and the Middle Ages, with seers like Nostradamus appearing to peek into the future, the idea of an ultimate destiny has become an obsession for many. Only nowadays do we have the scientific tools coupled with ultra-fast processing power necessary to make a well-substantiated picture of the distant future of the Solar System, which seems harbor large uncertainties for this planet. With the greatly increased radiation of an evolving Sun, our survival comes into question . . . Expansion of the Sun in the future will cause conditions to be vastly different from those today, leaving the Earth unsustainable. This study intends to establish which Solar System object will be most conducive to the survival of humans during five stages of solar evolution: (1) further along the main sequence at age 8.40 billion years (Ga), (2) during the red giant stage at 11.93 Ga (3) 6 million years (Ma) later prior to the helium flash (4) after the helium flash at age 12.17 Ga and (5) the beginning of core crystallization at age 12.23 Ga. The Evolve ZAMS code (Paxton, 2004) determines the mass and luminosity of the Sun at these stages. Semi-major axis lengths of each of the solar system objects (SSOs) are calculated based on mass loss (Schroder and Smith, 2008) and the principle of conservation of angular momentum. The potentially sustainable objects’ temperatures are solved for using blackbody equations, from which comparison of RMS gas speed with escape velocity determines the ability of a body to retain an atmosphere consisting of a specific gas. It is found that Earth and Mars are optimal SSOs in stage 1. In stages 2 and 3, Triton is most sustainable, but in stage 4, the Galilean moons and Titan appear to be more habitable. Stage 5 has Triton being the most optimal…

Cold Fusion has been an active research field in the quest for next-generation energy. In Andrei Lipson’s CR-39 experiments, oscillating deuterium atoms or other particles were accelerated (collective acceleration effect) through an electric field and collided with each other to undergo fusion. Another procedure conducted by Roussetski involved the bombardment of TiD2 with a Deuteron beam. In all these scenarios of fusion research, a significant bottleneck is the detection of reactant molecules. The application of CR-39 plastic track detectors in cold fusion experiments is vital to detecting and identifying different particles and background/foreground separation.The current method of gathering data from CR-39 tracks is to use an electron microscope to dissect each individual crater in the x-y and z planes. There has been no way to analyze large amounts of CR-39 data in a reasonable time frame. In this research, we study 3D trace data from nuclear particle impacts upon CR-39 detectors to identify craters made by particles. We utilize a new process, confocal microscopy, to gather numerical trace data from the polycarbonate. We propose and apply new approaches for detecting and computing several main characteristics, such as depth and incident angle, of the impact of the particle. Our approach and related code serves as a tool for automatically classifying the craters and matching them to known collision types and corresponding particles, therefore enabling the efficient and accurate processing of large quantities of CR-39 data…

I hear like an 85-year-old man, but I am not alone. Twenty-five million Americans are already affected by hearing loss (Hearing lost statistics), and this staggering number is expected to double by 2050 (qtd. in Schmid), especially considering how many students are currently damaging their ears by the combination of loud music and earphones. What they do not realize is that sound has a physical force that damages the stereocilia, the delicate hair cells in the cochlea that pick up vibrations. Once broken, those cells do not regenerate. The vast majority of people can expect hearing damage as they age. Others, like me, have damage from ototoxins; life-saving drugs like the ones that saved my life as a premature infant can cause unfortunate hearing impairment. That is the personal problem that led to my two-year science project, Do You =ear What I =ear?, which explores the revolutionary concept of lowering sounds in pitch rather than simply making them louder. Current hearing aid technology is still based on increasing the volume; however, I know from personal experience that hearing aids really do not work well…

As I opened up the local section, I saw an image of a tennis racket strung in a strange fashion. This intrigued me, so I decided to read the article. I soon discovered that several years earlier a local woman named Madeline Hauptman had co-patented a diagonally strung tennis racket featuring opposite pairs of equidistant strings strung in a diagonal fashion. She claimed that as a result of this congruency of string length, vibrations are more evenly dispersed following a tennis shot, reducing the level of vibration directed onto a given player’s forearm and possibly preventing tennis elbow. The article I was reading was a profile of PowerAngle, Mrs. Hauptman’s small diagonally strung racket company. I immediately rushed to my computer to find out some more information on PowerAngle. To my excitement, I found out that Mrs. Hauptman’s diagonally strung tennis rackets had never been scientifically tested or compared to conventional rackets.

One of the most exciting days of work occurred when I discovered that I could apply programming skills I acquired in my linear algebra class to my project. I needed a program that could graph in three dimensions, was easily manipulated, and used a color gradient to show height differences. MatLab, a matrix-based programming environment, fit that description perfectly.