
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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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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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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How much water do you use? Conserving water can do more than save your parents' money, it can also save freshwater ecosystems, wetlands, and watersheds. Some companies are trying to help fix the problem by making low flow faucets and showerheads. How well do they work? How much water can you save? Go to the hardware store to buy a few of the water saving products. Compare the amount of water that you run over a period of time to determine how much water you can save. Which water saving…
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EnvSci_p021
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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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How do you turn a 2dimentional piece of paper into a 3dimentional 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 3dimentional 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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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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Temperature also changes with latitude. As you move away from the equator, the temperature tends to decrease. Test this by comparing weather data from weather stations at different lattitudes. (FI, 2006; GLOBE, 2006; NCAR, 2006; NOAA, 2006; Unisys, 2006; Weather Underground, 2006; WMO, 2006)
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Weather_p021
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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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Using just a single sheet of paper (8.5 × 11 inches) and up to five paper clips, can you build a bridge that will span 20 cm and support the weight of 100 pennies? The area beneath the span must be free (so that boats can pass beneath it). To test your bridge, place two books 20 cm apart, and set the bridge on the books, spanning the gap. Do not fasten the bridge to the book (nor to any other support). Does your bridge hold as much weight as you expected it would? If your bridge fails…
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CE_p018
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