Try gluing wood together with different types of glue, e.g.: regular white glue, yellow wood glue, cyanoacrylate (super glue), and Liquid Nails. Glue a short piece (5-8 cm) to the center of a longer piece (15-30 cm). After the glue has dried for the recommended time, drill a small hole through the center of the joint, big enough to pass through a piece of coat-hanger wire. Cut a length of coat hanger wire, pass it through the hole, and twist the ends together to form a loop. Place the ends…
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How strongly do different types of nails hold in wood? Try different diameters of nails, and try pounding them to different depths. To gauge the holding strength, measure how difficult it is to remove the nail. Can you pull it out with a pair of pliers? Can you remove it with the hammer claw? Do you have to push only a little bit, moderately hard, or as hard as you can? Do you need a crowbar? What happens if you pre-drill holes for the nails, using drill bits that are different…
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How do you turn a 2-dimensional piece of paper into a 3-dimensional work of art? Origami, the classical art of Japanese paper folding, is loaded with mathematical themes and concepts. What are the common folds in origami, and how do they combine to create 3-dimensional structure? Can you classify different types of origami into classes based upon the types of folds they use? Can you show Kawasaki's Theorem, that if you add up the angle measurements of every other angle around a point, the sum…
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Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics.
Figure 1 below shows a series of circles (iC₁, iC₂, iC₃, ..., iC₃₀), inscribed inside an arbelos. What is an arbelos? The arbelos is the white region in the figure, bounded by three semicircles. The diameters of the three semicircles are all on the same line segment, AC,…
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Math_p011

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Time Required

Average (6-10 days)

Prerequisites

Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination

If you have a multi-speed bike, you know that you can make it easier or harder to pedal just by shifting gears. Ever wonder how that works? You can investigate this a number of ways. A basic approach is to use a selection of spools of thread (with different diameters), a board with two nails, and a rubber band. Place a spool over each nail, and put the rubber band over them. Mark the 12:00 position on each spool so that you can count revolutions. Turn one spool through a full circle and…
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Get good photographs of the Moon showing lots of craters and count how many craters you find in a range of diameter classes. One useful source is the (Kuiper et al, 2006). Make a histogram that shows the distribution of diameters. Most of these craters were formed during the first billion years of the Moon's formation, but you should confirm that this is true for the the Moon areas you've selected in your photographs by doing background research. Is cratering uniform across the surface of the…
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Learn how to edit sound files so that you can manipulate the recorded sound mathematically. You can either find specialized audio editing software or do background research to teach yourself about sound file structure so that you can write your own simple program to manipulate sound files. Try arithmetic operations on the sound values (e.g., adding or subtracting a constant, multiplying or dividing by a constant). How do these operations alter the sound? Try other mathematical operations:…
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Make a pinhole projector (see ). 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 and falls with an 11-year cycle. At this…
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How much force is required to advance a lag bolt (large wood screw with a hex-shaped head) into a piece of wood? You can measure the force by using a spring scale attached to the handle of ratchet. Pull on the spring scale until the bolt starts to turn, and note the required force from the spring scale. There are many potential experiments you could try. Think about answering the following questions: How does the force change as the bolt advances deeper into the wood? Why? How does the…
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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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