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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)
Project Idea
Imagine a symmetrical grid of nine points superimposed over the ball. Kicking the ball squarely on the center point imparts no spin, but kicking on any of the other points will impart spin on the ball. How will the resulting spin affect the trajectory of the ball for each of the 8 outer grid points? Kicking the ball with a sliding motion of the foot is another way to impart spin. Once you've made your predictions, you can set up to test them with a soccer ball, video camera and a tape… Read more
Sports_p031
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Time Required Average (6-10 days)
Project Idea
Students who are mathematically inclined can use the student version of a program like MatLab or Mathematica to convert a digital image into numbers, then perform operations such as sharpening or special effects. This is a great way to learn about image processing algorithms. Read more
Photo_p018
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Time Required Long (2-4 weeks)
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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Here's an interesting project idea with a variation that combines computer science, physics and music. You'll need a piano in a quiet room, a microphone and a computer with digital sound recording and analysis software. The project shows you how you can make a piano string start vibrating without hitting its key. You can record the sounds on the computer, and use sound analysis software to measure the frequencies of the induced vibrations. For more details see: How to Make a Piano Sing. Be… Read more
CompSci_p026
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Time Required Long (2-4 weeks)
Project Idea
Some claim the Moon appears larger when near the horizon. Make a series of observations of the Moon, measuring the Moon's angular diameter each time. You should also note the Moon's altitude above the horizon, and the Moon's phase. You should do background research on the lunar orbit to determine the necessary time period. Do you find predictable variations in the Moon's diameter? Can you relate this to the Moon's changing distance from Earth? From your data, try to determine when apogee and… Read more
Astro_p030
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Time Required Very Long (1+ months)
Project Idea
Want to send coded messages to your friends? Can you write a simple letter-substitution encryption program in JavaScript? How easy is it to break the simple code? Can you write a second program that "cracks" the letter-substitution code? Investigate other encryption schemes. What types of encryption are least vulnerable to attack? Read more
CompSci_p031
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Time Required Long (2-4 weeks)
Project Idea
Some laundry detergents have added enzymes that break down proteins, helping to remove them from the cloth fibers, and thus remove stains. You can perform a scientific test of these enzymes' stain-fighting ability. Do background research on the enzyme(s) in the detergent, and on the substances you choose for making the stains. Try to predict for which substances the enzymes will be effective. Cut a piece of light-colored cotton cloth into identical 10-cm squares. Choose different types of… Read more
Chem_p039
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Time Required Very Short (≤ 1 day)
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Beats are a pattern of oscillating sound intensity (i.e., the volume of the pattern grows and fades with a regular cycle). They occur when two tones of almost equal frequency interfere. People can perceive beat frequencies below about 7 Hz. Figure out how to create sound files to play pure tones on your computer. Create files with a pure tone of one frequency in the left channel, and a pure tone of a different frequency in the right channel. Systematically explore different frequency… Read more
Music_p001
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Time Required Long (2-4 weeks)
Project Idea
Use sound recording and analysis software to record voices of your family members. Can you figure out ways to identify each family member by just looking at the analyzed sound patterns from their voice (e.g., spectral frequency analysis)? Develop a hypothesis about what types of sound analysis will identify an individual. Have a helper record additional test files of your family members, without telling you which file belongs to whom. Unplug your computer speakers and see if you can… Read more
CompSci_p027
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Time Required Average (6-10 days)
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