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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 super-advanced mathematical genius, try to evaluate currently available, logic-based computational tools, or design a better one!… Read more
Math_p035
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Time Required Average (6-10 days)
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… Read more
Math_p028
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Time Required Average (6-10 days)
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… Read more
Math_p036
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Time Required Average (6-10 days)
Science Fair Project Idea
How do you turn a 2-dimensional piece of paper into a 3-dimensional 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 3-dimensional 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… Read more
Math_p032
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Time Required Long (2-4 weeks)
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… Read more
Math_p031
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Time Required Long (2-4 weeks)
Science Fair Project Idea
Here's a project that will teach you about math as you follow some of your favorite players or teams. You'll be comparing day-to-day performance with long-term averages, and trying to determine if the "streaks" and "slumps" over shorter time periods are due to random chance or something else. When you've finished, you'll have a better understanding of some important concepts in statistical analysis and baseball. If a player goes 0-for-20, does that mean anything? Using probability theory,… Read more
Math_p004
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Time Required Average (6-10 days)
Prerequisites Basic knowledge of Microsoft Excel and statistics
Material Availability Readily Available
Cost Very Low (under $20)
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 "Well-Tempered-Scale" or the "Equal-Tempered-Scale", is based upon a series. How are these mathematical series and ratios related to notes, chords, intervals, and octaves? You can… Read more
Math_p034
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Time Required Average (6-10 days)
Science Fair Project Idea
Is winning correlated with fun? Pick a video game which has different difficulty settings, for example easy versus hard mode. Ask volunteers who have never played the game before to try it out. Some of them should use the easy mode and others should use the hard mode, this will ensure that you have a range in the amount of winning and losing among your volunteers. Keep track of how much each player is winning. Survey the volunteers to find out if they like the game. Do people who win more like… Read more
Games_p010
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Time Required Average (6-10 days)
Prerequisites None
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
Science Fair Project Idea
What makes a winning team? Getting all the best players? Good coaches? Good chemistry? This project will show you how you can use math to help you test your hypothesis about what makes a winning team. The Pythagorean relationship is a fundamental one in sports: it correctly predicts the records of 98% of all teams. But in 2% of cases, it fails. Why does it fail? Find teams that deviated substantially from their expected Pythagorean record (this information is available for baseball teams… Read more
Math_p005
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Time Required Average (6-10 days)
Prerequisites Basic knowledge of Microsoft Excel and statistics
Material Availability Readily Available
Cost Very Low (under $20)
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 rubber-sheet 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… Read more
Math_p030
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Time Required Average (6-10 days)
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