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

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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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 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

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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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

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

The Falkirk Wheel is a rotating boat lift connecting the Forth and Clyde Canal with the Union Canal near Falkirk in central Scotland. It consists of two diametrically opposed caissons which rotate to lift boats between the two canals through a height of 35 meters. The wheel is always perfectly balanced and, despite its enormous mass, rotates through 180° in less than four minutes, using just 1.5 kilowatthours (Wikipedia contributors, 2006). Do background research to find out how much energy…
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Energy_p006
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Science Fair Project Idea

Math is used by many different types of scientists to model phenomenon and evaluate data from an experiment. By building mathematical models scientists can understand how different physical, chemical, and biological processes are affected by different variables. The most important tools are: making a graph to give a visual representation of the relationships between your variables and making an equation to give a way of computing the relationships between your variables. Find a source of data,…
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Math_p029
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Science Fair Project Idea

In the U.S., lighting homes and businesses accounts for 22% of all electric power consumption (Raloff, 2006). That's $55 billion worth of electricity, or the output of 100 large power plants (Raloff, 2006). How much energy could be saved by switching home lighting from incandescent to more efficient fluorescent lights? Conduct a survey to find out what types of lighting are used in homes in your area. Come up with an estimate of how many light fixtures are used in an average home, what types…
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Energy_p005
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Short (25 days) 
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