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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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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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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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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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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 beyond…
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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 two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player…
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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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