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Others Like “Divide and Conquer: Proving Pick's Theorem for Lattice Polygons”

Project Idea
thumbnail Although fractal images can be intriguingly complex, fractals are more than just pretty pictures. In this project, you'll explore the mathematical properties of the famous Mandelbrot (illustration at right) and Julia sets. You'll learn about how these images are generated, and about the relationship between the Mandelbrot set and the Julia sets. Read more
Math_p013
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Time Required Average (6-10 days)
Prerequisites Good understanding of algebra, excellent computer skills
Material Availability Computer with Internet access required
Cost Very Low (under $20)
Safety No issues
Project Idea
thumbnail Ok, well you won't be making real monkeys fly, so what's this science project all about? You might think that flying, screaming monkeys and science project do not belong in the same sentence, but you'll be working with toy monkeys, and toys can sometimes be great tools for exploring science. In this science project, you will launch flying, screaming toy monkeys and determine how far they fly with the stretch of a rubber band. The distance they'll go can be graphed to see how distance depends on… Read more
Aero_p045
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Time Required Average (6-10 days)
Prerequisites A large open space to launch the monkey is required.
Material Availability You will need to purchase the Flying Screaming Monkey toy. See the Materials and Equipment list for details.
Cost Low ($20 - $50)
Safety No issues
Project Idea
thumbnail Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics. Read more
Math_p011
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- Less Details
Time Required Average (6-10 days)
Prerequisites Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
Project Idea
thumbnail The banjo's roots trace all the way over to Africa. The unique sound that a banjo makes depends, in part, on the resonator. The purpose of the resonator is to amplify and project the sound that is made by strumming and plucking the strings. In this music science fair project, you will experiment with a resonator on a banjo and see if you can hear the difference in sound. Read more
Music_p029
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Time Required Average (6-10 days)
Prerequisites You must have access to a computer with a microphone, a spreadsheet program,and an Internet connection. You need to have a basic proficiency with and be able to graph data in the spreadsheet program. If you need help, consult a help guide online or find an adult who is familiar with the spreadsheet program you are using.
Material Availability Readily available
Cost Low ($20 - $50)
Safety Minor injury is possible. Always wear safety goggles and use caution when using tools. Adult supervision is required.
Project Idea
thumbnail This is an interesting geometry project that goes back to the time of Archimedes, the famous Greek mathematician. You can combine this mathematical project with computer science and take this ancient problem into the twenty-first century with a dynamic diagram using the geometry applet. Read more
Math_p018
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Time Required Short (2-5 days)
Prerequisites You should either currently be taking or have already completed a first course in geometry. You must understand the concept and method of a mathematical proof.
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
Project Idea
thumbnail In physics class, you have probably rolled your eyes at some point after being assigned a "projectile motion" homework problem where you use equations to predict how a ball will move through the air. This experiment will show you just how fun that problem can be by using a real catapult to launch a ball and videotaping it as it flies along its path. Then, you will analyze the video and compare it to what the equations predicted. If you have ever wondered if those equations in your physics… Read more
Phys_p089
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Time Required Average (6-10 days)
Prerequisites This project requires a basic understanding of algebra, trigonometry (sine and cosine functions), and physics (kinematics—two-dimensional projectile motion), or the willingness to learn about these subjects on your own.
Material Availability This project requires access to a video camera (not included in the cost estimate) and the purchase of a catapult kit. (See the Materials and Equipment list for details.)
Cost Average ($40 - $80)
Safety Minor injury possible. Never aim the catapult at anyone, and keep your hands and fingers clear of the moving catapult arm when launching the catapult.
Project Idea
thumbnail Have you ever tried to ride your bike up a flight of stairs? Vehicles with wheels are great at traveling on paved roads or flat ground, but when it comes to stairs or uneven ground in the woods, wheels are not always such a great option. Inspired by real-life all-terrain robots, in this engineering project you will design and build a LEGO® robot that can travel over bumpy ground, through your yard, or even up a stack of textbooks — and almost anything else you can think of! Read more
Robotics_p009
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Time Required Average (6-10 days)
Prerequisites Experience building with LEGO® and programming for LEGO® Mindstorms® is required for this project.
Material Availability This project requires a LEGO® Mindstorms® NXT kit and compatible programming software. See the Materials and Equipment list for details.
Cost Very High (over $150)
Safety No issues
Project Idea
thumbnail Have you ever wanted to analyze data from a NASA spacecraft? In this science project you will use data from NASA's MESSENGER mission to measure the diameter and calculate the depth of impact craters on Mercury. You will then analyze that data for relationships between a crater's depth and diameter. This is your chance to perform a science project as a NASA researcher would! Read more
Astro_p036
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Time Required Very Short (≤ 1 day)
Prerequisites Geometry: familiarity using sine, cosine, and tangent to solve right triangles
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
Project Idea
thumbnail If you have ever tried to hit a target (such as a trash can) with a wad of paper, you know that aim is everything. But it is not always easy to get it right every time! Missing is not that big a deal with a wad of paper, but what if you were in an invading army in the Middle Ages, using a catapult to hurl huge stones and knock down castle walls? For a successful invasion, it would be important to know exactly how far, and how reliably, a catapult could launch a projectile. In this project you… Read more
Math_p046
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Time Required Average (6-10 days)
Prerequisites An introductory-level understanding of statistics (mean, standard deviation, and the normal distribution) is helpful, but not required for completing this project.
Material Availability Requires catapult kit. See the Materials and Equipment list for details.
Cost Average ($40 - $80)
Safety Do not aim the catapult at people or breakable objects; minor injury possible.
Project Idea
thumbnail This is an interesting project that explores which geometrical shapes make the strongest bridge truss structures. It is a good introduction to the engineering design process. You'll design three different trusses, and use online simulation software to analyze the distribution of load-bearing forces in each design. Then you'll build and test prototypes of each design. Read more
CE_p006
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Time Required Average (6-10 days)
Prerequisites Excellent computer skills, high school physics course
Material Availability Readily available
Cost Low ($20 - $50)
Safety Use caution with sharp tools when cutting wooden parts to size. Adult supervision recommended for bridge-testing phase.
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