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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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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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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A solution consists of a solute dissolved in a solvent. A solution is saturated when no additional solute will dissolve in it. Can a saturated solution of sodium chloride dissolve any Epsom salts? Can a saturated solution of Epsom salts dissolve any sodium chloride? How does solubility vary with temperature? How does solubility vary with the surface area of the solute? Design experiments to find out! (Gardner, 1999, 16-17, Stretton, 2004)
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How much difference does the spiraling motion of a well-thrown football make on the distance of the throw (compared to wobbling, or end-over-end motion of the ball)? Think of a way to reproducibly produce the desired ball motion and launch it with a constant force to find out. (For more information on the physics, see Gay, 2004.)
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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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You probably know that you can use iron filings to reveal the magnetic field produced by a strong magnet. If you sandwich the iron filings between pieces of waxed paper, you can make a permanent record of your magnetic experiments (Gardner, 2004, 66). Cover the wax paper sandwich with a layer of brown paper (from a roll, or cut open a paper shopping bag), and then (with an adult's help) use a hot, dry iron to seal the waxed paper together. You will have to experiment a little with your iron…
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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 "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…
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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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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!…
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