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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)
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)
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)
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 two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player… Read more
Math_p033
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Time Required Average (6-10 days)
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How do you turn a 2-dimentional piece of paper into a 3-dimentional 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-dimentional 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)
Project Idea
Sudoku puzzles have become extremely popular over the past couple of years. You can find books of puzzles for beginners to experts, and many newspapers print Sudoku puzzles daily. This project challenges you to write a computer program to check if your Sudoku solution is correct. Read more
CompSci_p023
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Time Required Average (6-10 days)
Prerequisites An understanding of the material covered in "ABC's of Programming: Writing a Simple 'Alphabetizer' with JavaScript."
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues
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… Read more
Math_p027
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Time Required Short (2-5 days)
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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… Read more
Math_p031
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Time Required Long (2-4 weeks)
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)
Project Idea
thumbnail Did you know that in addition to the Sun and planets, our solar system is filled with millions of asteroids, which are chunks of rock left over from the early days of its formation, or from collisions between larger objects like planets? Agencies like NASA track asteroids, not only because they might pose a threat to humanity by colliding with Earth, but because they can provide us with information about the history of our solar system, and even be useful for mining raw materials in space! In… Read more
Astro_p039
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Time Required Short (2-5 days)
Prerequisites In order to do this science project, you should either already have knowledge of basic statistical analysis (histograms and scatter plots) or have a willingness to familiarize yourself with them.
Material Availability This science project requires a computer with internet access and a spreadsheet program like Microsoft® Excel® or OpenOffice™ Calc.
Cost Very Low (under $20)
Safety No issues
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