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…
What makes a winning team? Getting all the best players? Good coaches? Good chemistry? This project will show you how you can use math to help you test your hypothesis about what makes a winning team.
The Pythagorean relationship is a fundamental one in sports: it correctly predicts the records of 98% of all teams. But in 2% of cases, it fails. Why does it fail? Find teams that deviated substantially from their expected Pythagorean record (this information is available for baseball teams…
You can compare the picture quality for photos taken at different shutter speeds with the camera handheld vs. with the camera on a tripod. (This is best done with a camera that has manual exposure control.)
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…
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…
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…
The different species of wood used in construction offer a variety of challenges based on density, porosity, oils in the wood, flexibility, elasticity, etc. The intended use, e.g., structural or cosmetic, presents different challenges as well. The glue must be compatible with the wood, the use, and the climate, so many experiments are possible. For example, you could design an experiment to test the durability of different adhesives using the same wood. Or, you could try different wood…
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…
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…
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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Average (6-10 days)
Good grasp of Euclidean geometry, a firm understanding of how to construct a mathematical proof, determination
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