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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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Average (610 days) 
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Science Fair Project Idea

How do you turn a 2dimensional piece of paper into a 3dimensional 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 3dimensional 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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Science Fair Project Idea

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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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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Science Fair Project Idea

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 beyond…
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Math_p031
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Science Fair Project Idea

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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Average (610 days) 
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Access to a homemade wind tunnel 
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Readily available 
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Science Fair Project Idea

What do knots, maps, mazes, driving directions, and doughnuts have in common? The answer is topology, a branch of mathematics that studies the spatial properties and connections of an object. Topology has sometimes been called rubbersheet geometry because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without…
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Math_p030
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Science Fair Project Idea

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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Science Fair Project Idea

You can model this with an ice cube sliding down a plank: how high do you need to lift the end of the plank before the ice cube starts to slide? Try this with one side plain wood and the flip side waxed wood (use paraffin wax, candle wax or ski wax). Make sure both sides are equally smooth to start with. Do at least three trials. More advanced: using what you know about the forces acting on the ice cube, derive equations to calculate the coefficient of friction for each case. Variation:…
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Sports_p042
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Short (25 days) 
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Science Fair Project Idea

How does ski wax affect the sliding friction of skis? You can model this with an ice cube sliding down a plank: how high do you need to lift the end of the plank before the ice cube starts to slide? Try this with one side plain wood and the flip side waxed wood (use paraffin wax, candle wax or ski wax). Make sure both sides are equally smooth to start with. Do at least three trials. More advanced: using what you know about the forces acting on the ice cube, derive equations to calculate the…
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ApMech_p031
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