Others Like “Divide and Conquer: Proving Pick's Theorem for Lattice Polygons” (top 20 results)
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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…
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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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Aerodynamics and Hockey: Does the Force of Drag Have an Effect on the Distance the Puck Will Travel?
Think of a way to launch the puck with a reproducible force, and examine the effect of launching the puck in different orientations on the distance it travels. For more information on the physics, see Haché, 2002.
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We've all heard that "practice makes perfect," but what is the best way to practice? For example, does "mental practice" do any good? You'll need at least 9 volunteers for this project. Pick a well-defined sports activity, with a measurable outcome, such as shooting basketball free-throws (measure number of shots taken and number of shots made), or balancing on one foot on a slightly raised beam (measure how long you can do it; if it's too easy, try closing your eyes). Test all volunteers…
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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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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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Use your Internet sleuthing skills to learn about solar system objects. Create a table of measurements of moons and asteroids in order to determine if there is a size threshold for roundness. A good source of information would be an online guide such as The Nine Planets (Arnett, W.A., 2006). You'll find information about planetary satellites, including dimensions and accompanying pictures. From the pictures, classify the satellites and asteroids according to how round they are. Can you think of…
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Make a pinhole projector (see Measuring the Diameter of the Sun and the Moon). Use the pinhole to project an image of the Sun onto a wall or a piece of paper. Do you notice any dark spots on the projected image? Trace the projected image and count the dark spots. Use your pinhole projector to make images of the Sun at the same time of day for several consecutive days. How does the pattern of spots change? Can you use your data to figure out how fast the Sun rotates? Sunspot activity rises…
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This project can apply to soccer, hockey, baseball and many other sports. What is the effect of stopping the kick/shot/swing at the moment of impact vs. following through? Think of a way to measure the outcome in each case, and explain your results. (idea from Gardner, 2000, 83-85; for more information with regard to specific sports, see: Barr, 1990, 12-14; Gay, 2004, 142-144; Adair, 2002, 30.)
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Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? 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…
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