
Have you ever flown in an airplane, or looked up at one flying in the sky, and wondered how such a massive machine can stay in the air? Airplanes can stay in the air because their wings, also referred to as airfoils, generate lift. Engineers use devices called wind tunnels to experiment and test different wing shapes when they design new airplanes. Wind tunnels let engineers make careful measurements of the air flow around the wing, and measure the amount of lift it generates.
If you can get…
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Aero_p004
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Time Required 
Average (610 days) 
Prerequisites 
Access to a homemade wind tunnel 
Material Availability 
Readily available 
Cost 
Average ($50  $100) 
Safety 


How do you turn a 2dimentional piece of paper into a 3dimentional work of art? Origami, the classical art of Japanese paper folding, is loaded with mathematical themes and concepts. What are the common folds in origami, and how do they combine to create 3dimentional structure? Can you classify different types of origami into classes based upon the types of folds they use? Can you show Kawasaki's Theorem, that if you add up the angle measurements of every other angle around a point, the sum…
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Math_p032
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Long (24 weeks) 
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Music has many mathematical elements in it: rhythm, pitch, scale, frequency, interval, and ratio. There are many ways to turn these elements into a science fair project. You can investigate how the scale is based upon a special type of number sequence called a Harmonic Series. Another scale used by Bach, called the "WellTemperedScale" or the "EqualTemperedScale", is based upon a series. How are these mathematical series and ratios related to notes, chords, intervals, and octaves? You can…
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Math_p034
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Average (610 days) 
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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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Average (610 days) 
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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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Average (610 days) 
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A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole"
(Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in complexity as it is generated through repeated sets of numbers called iterations. There are many interesting projects exploring fractal geometry that go…
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Math_p031
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Long (24 weeks) 
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This project challenges you to figure out how to make geometric patterns with Rubik's Cube. Leaving your cube in one of these positions makes it much more tempting to pick it up and 'fix' it. Can you figure out how to make a checkerboard, or a cubewithinacube? Can you make only the center piece a different color from the rest? Can you figure out how to solve the cube from these positions?
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Math_p024
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Time Required 
Long (24 weeks) 
Prerequisites 
To do this project you should enjoy solving puzzles and thinking in three dimensions. This project requires starting with Rubik's Cube in the solved position, so you will need to know how to solve the puzzle in order to do this project. 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 

If you're the kind of person who has taken apart your Rubik's cube in order to grease the inside parts so it will move more smoothly, this could be a great project for you. We'll show you three sets of move sequences that accomplish specific rearrangements of the cube. Can you devise a way to solve the cube using only these three move sequences?
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Math_p025
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Time Required 
Long (24 weeks) 
Prerequisites 
To do this project you should enjoy solving puzzles and thinking in three dimensions. 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 

Kites have been a source of entertainment for centuries for kids from cultures around the world. In this science project you will have a chance to build your very own kite, a simple sled kite. Then you will use it to investigate how kites fly. Will you find out the best way to fly your kite?
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Aero_p016
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Time Required 
Very Short (≤ 1 day) 
Prerequisites 
None 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 

A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be n(n2+1)/2? Are there any other hidden properties of a…
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Math_p036
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Time Required 
Average (610 days) 
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