Others Like “Magic Squares” (top 20 results)
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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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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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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You can measure the diameter of the Sun (and Moon) with a pinhole and a ruler! All you need to know is some simple geometry and the average distance between the Earth and Sun (or Moon). An easy way to make a pinhole is to cut a square hole (2-3 cm across) in the center of a piece of cardboard. Carefully tape a piece of aluminum foil flat over the hole. Use a sharp pin or needle to poke a tiny hole in the center of the foil. Use the pinhole to project an image of the Sun onto a wall or piece…
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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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When the punter is trying to hit the "coffin corner" (within the opposing team's 10-yard line), out of bounds, what is the best angle to kick the ball for correct distance and maximum "hang time?" (For more information on the physics involved, see: Gay, 2004, Chapters 4 and 5.)
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Let's suppose you can take advantage of the Internet and get a 'pen pal' located a 1000 miles away in another city. On the same night, and at EXACTLY the same time 'Universal Time', make a CAREFUL observation of where the Moon is located with respect to the background stars. You should be able to discern a slight (about 1/2 the Moon's diameter) shift in position due to parallax. Then, with a little geometry, you could estimate the distance of the Moon during the full lunar cycle (Odenwald,…
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Place a desk chair (one that rotates easily on ball bearings) in the center of the room, away from any obstructions. Put your hands on your lap and have a helper give you a push to start you rotating. You'll need to quantify the results somehow. For example, your helper could measure the number of revolutions you make in 5 seconds. Now try extending your arms after your helper starts you spinning. Next, start with your arms out, and bring them in close to your body after you start…
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The Science Buddies project Design Your Own 3D Printed Optical Illusion shows you how to make your own 3D printed "anomalous mirror symmetry" illusions (Figure 1). The illusions are based on the work of Dr. Kokichi Sugihara. You can read his original paper about the illusions in the Bibliography.
Figure 1. Two versions of the "impossible arrow" shape that appears to point to the right while its reflection in the mirror appears to point to the left. Which…
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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