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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Average (610 days) 
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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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Time Required 
Average (610 days) 
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Science Fair Project Idea

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 twentyfirst century with a dynamic diagram using the geometry applet.
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Math_p018
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Time Required 
Short (25 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 
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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Average (610 days) 
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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

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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Time Required 
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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Time Required 
Long (24 weeks) 
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Science Fair Project Idea

Here is a project that combines Computer Science and Mathematics. Prove a method for circumscribing a circle about a triangle (as shown). You'll also learn how to create an interactive diagram to illustrate your proof, using an applet that runs in your Web browser. If you like solving problems and thinking logically, you'll like this project.
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CompSci_p007
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Time Required 
Short (25 days) 
Prerequisites 
Must understand the concept and method of a mathematical proof 
Material Availability 
Readily available (laptop computer helpful for live demonstration) 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

Many industries rely on scale models to develop new products and designs. Architects, industrial designers, artists, clothing designers, and car manufacturers all use scale models. Each model is built to a scale that relates the actual object to the model through a ratio. Can you determine a formula for constructing a scale model? You can use your formula to make a model of your house, school, neighborhood, or town (CUBE, 2002). You can make scale models of the Wright Brothers aircraft…
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Math_p028
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