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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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Average (610 days) 
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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

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 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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Long (24 weeks) 
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Science Fair Project Idea

The Game of Life is the invention of the mathematician John Conway. It is a cellular automaton, consisting of a grid of squares that turn "on" or "off" depending on simple mathematical rules that involve neighboring squares. Depending on how the grid is first set up (i.e., the initial conditions), various interesting patterns appear. Can you write a Game of Life program (in JavaScript or any other computer language of your choice)? Can you think of ways to alter the rules that result in…
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CompSci_p030
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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

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

Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics.
Figure 1 below shows a series of circles (iC₁, iC₂, iC₃, ..., iC₃₀), inscribed inside an arbelos. What is an arbelos? The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AC,…
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Math_p011
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Time Required 
Average (610 days) 
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Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination 
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Readily available 
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Very Low (under $20) 
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No issues 
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 
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Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 

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