
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.
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Photo_p018
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Long (24 weeks) 
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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…
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Music_p001
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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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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…
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CompSci_p027
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Research the famous collapse of the Tacoma Narrows suspension bridge.
What lessons were learned about the potentially damaging effects of wind on bridges? What structures stabilize a bridge against wind forces? Build models and use a wind tunnel to test your hypothesis.
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Aero_p030
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Math is used by many different types of scientists to model phenomenon and evaluate data from an experiment. By building mathematical models scientists can understand how different physical, chemical, and biological processes are affected by different variables. The most important tools are: making a graph to give a visual representation of the relationships between your variables and making an equation to give a way of computing the relationships between your variables. Find a source of data,…
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Math_p029
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What are the best materials to use for blocking out unwanted noise from the environment? You can build a test box (or test frame) around an audio speaker. Use a sound level meter to measure the speaker output. Use different materials to cover the walls of your test box (or frame), and see which materials do the best job at blocking the sound. For a more advanced project, perform your tests using different sound frequencies. Are some materials better at blocking certain frequencies than…
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MatlSci_p033
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The Game of Life is the invention of the mathematician John Conway. It is a cellular automaton, consisting of a grid of squares that turn "on" or "off" depending on simple mathematical rules that involve neighboring squares. Depending on how the grid is first set up (i.e., the initial conditions), various interesting patterns appear. Can you write a Game of Life program (in JavaScript or any other computer language of your choice)? Can you think of ways to alter the rules that result in…
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CompSci_p030
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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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Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced project: Use your knowledge of geometry and basketball to come up with a mathematical expression to predict your success rate as a function of angle…
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Math_p037
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Short (25 days) 
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