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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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…
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Your digital photo comprises a certain number of dots in the x and y directions. What happens to the print image quality as you "stretch" those dots out to larger and larger pictures? (Note: This experiment studies the dots per inch in the image itself, not the number of dots per inch that is output by your printer.)
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For example, think of hitting a baseball, heading a soccer ball into the net, or hitting a tennis ball with a racquet. Where the ball goes depends on...what? You can set up a simple model to start your investigation. You'll need a marble, a flat piece of wood, a flat piece of cardboard, a pencil, a ruler, a protractor, and a level surface. Lay down the cardboard down on a level surface and set up the flat piece of wood at one edge. The wood will act like a wall, and you're going to roll…
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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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Think of hitting a baseball, heading a soccer ball into the net, or hitting a tennis ball with a racquet. Where the ball goes depends on...what? You can set up a simple model to start your investigation. You'll need a marble, a flat piece of wood, a flat piece of cardboard, a pencil, a ruler, a protractor, and a level surface. Lay down the cardboard down on a level surface and set up the flat piece of wood at one edge. The wood will act like a wall, and you're going to roll the marble at…
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A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an algorithm for constructing a Magic Square? Can you show that the sum of the entries of any row, column, or main diagonal must be n(n2+1)/2? Are there any other hidden properties of a…
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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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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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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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