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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) 
Prerequisites 
Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No issues 
Science Fair Project Idea

Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in different types of bank accounts. How much better is a savings account than a checking account? What difference does the interest rate make? Which is better, an account that earns compound or simple interest? Can you compare the short and long term costs of borrowing money compared to saving the cash…
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Math_p027
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Time Required 
Short (25 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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Average (610 days) 
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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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Time Required 
Long (24 weeks) 
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Science Fair Project Idea

If you've played catch with both Aerobie flying rings and Frisbees, you know that the rings fly much further than the Frisbees with the same throwing effort. Why is that? Investigate the aerodynamics of flying rings and flying disks and find out!
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Aero_p011
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Time Required 
Average (610 days) 
Prerequisites 
None 
Material Availability 
Readily available 
Cost 
Very Low (under $20) 
Safety 
No hazards 
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

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

If you like to play Tetris, then you might like this project. You will learn something interesting about the mathematics of complex shapes as you try to prove Pick's Theorem.
The strange shape below is an example of a lattice polygon, which is a polygon whose vertices lie on points in the plane that have integer coordinates.
As you can see, it is a complex shape, but there is an easy way to calculate its area, by simply counting lattice points!
If you count the number of lattice points on…
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Math_p009
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Time Required 
Short (25 days) 
Prerequisites 
None 
Material Availability 
Readily available 
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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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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Average (610 days) 
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