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Science Fair Project Idea

This a straightforward, but interesting, project in geometry. It is a good first proof to try on your own. You should be able to figure it out by yourself, and you'll gain insight into a basic property of circles.
Figure 1 below shows a semicircle (AE, in red) with a series of smaller semicircles (AB, BC, CD, DE, in blue) constructed inside it. As you can see, the sum of the diameters of the four smaller semicircles is equal to the diameter of the large semicircle. The area of the larger…
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Math_p010
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Time Required 
Very Short (≤ 1 day) 
Prerequisites 
Must understand the concept of a mathematical proof 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

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 on the Background tab) and Julia sets. You'll learn about how these images are generated, and about the relationship between the Mandelbrot set and the Julia sets.
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Math_p013
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Time Required 
Average (610 days) 
Prerequisites 
Good understanding of algebra, excellent computer skills 
Material Availability 
Computer with Internet access required 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win twoplayer games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multiplayer…
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Math_p033
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Time Required 
Average (610 days) 
Prerequisites 

Material Availability 

Cost 

Safety 

Science Fair Project Idea

If you like to play Tetris, then you might like this project. You will learn something interesting about the mathematics of complex shapes as you try to prove Pick's Theorem.
The strange shape below is an example of a lattice polygon, which is a polygon whose vertices lie on points in the plane that have integer coordinates.
As you can see, it is a complex shape, but there is an easy way to calculate its area, by simply counting lattice points!
If you count the number of lattice points on…
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Math_p009
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 Less Details
Time Required 
Short (25 days) 
Prerequisites 
None 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

You can see examples of parabolic reflectors in flashlights, car headlights, satellite TV antennas, and even on the sidelines at football games. How do these "dish" antennas work to gather signals? What is the best position for placing the detector for these antennas? In this project, you can use an LED and a simple photodetector to find out for yourself.
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Elec_p040
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Time Required 
Long (24 weeks) 
Prerequisites 
None 
Material Availability 
Specialty items 
Cost 
Average ($50  $100) 
Safety 
No issues 
Science Fair Project Idea

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…
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Math_p046
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Time Required 
Average (610 days) 
Prerequisites 
An introductorylevel 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. 
Science Fair Project Idea

This is a really fun project even if you don't like going on roller coasters yourself. You'll build a roller coaster track for marbles using foam pipe insulation and masking tape, and see how much of an initial drop is required to get the marble to "loop the loop." It's a great way to learn about how stored energy (potential energy) is converted into the energy of motion (kinetic energy).
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Phys_p036
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Time Required 
Short (25 days) 
Prerequisites 
None 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
Adult supervision recommended when using utility knife 
Science Fair Project Idea

If you've ever wondered how tall that bridge is, or how high your kite was, then this could be a good project for you. You'll learn how you can use the mathematics of right triangles to measure the height of an object with two measurements that you can make on the ground.
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Math_p026
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Time Required 
Short (25 days) 
Prerequisites 
None 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

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!
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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 
Science Fair Project Idea

You may know Lewis Carroll as the author of Alice in Wonderland, but did you know that in real life he was a mathematician who studied symbolic logic and logical reasoning? How can math help you solve Lewis Carroll's Logic Game? (Bogomolny, 2006) How are algorithms for solving the game Sudoku similar to solving a logic problem? (Hayes, 2006) For the superadvanced mathematical genius, try to evaluate currently available, logicbased computational tools, or design a better one!…
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Math_p035
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Time Required 
Average (610 days) 
Prerequisites 

Material Availability 

Cost 

Safety 


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