Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player…
Do you have a favorite picture? When you have a photo that you treasure, you want it to look as good as possible. Find out how the resolution of a digital photo effects the way it looks when you print it out. How does the quality of the image relate to the resolution?
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Very Short (≤ 1 day)
Requires photo editing software, a digital photo, and a color printer.
Using just a single sheet of paper (8.5 x 11 inches) and up to five paper clips, can you build a bridge that will span 20 cm and support the weight of 100 pennies? The area beneath the span must be free (so that boats can pass beneath it). To test your bridge, place two books 20 cm apart, and set the bridge on the books, spanning the gap. Do not fasten the bridge to the book (nor to any other support). Does your bridge hold as much weight as you expected it would? If your bridge fails…
Plant stems grow through a process of elongation due to cell divisions within the stem. Does the entire length of the stem elongate evenly? Or do certain regions along the plant stem grow more or less than others? Regions that are involved in active growth are called vegetative. You can conduct an experiment to show which regions of a bean seedling are involved in vegetative growth. Use a marker to mark one inch sections along the main stem of a young bean seedling. Number the regions 1-6…
Divide a part of your garden into two equal plots, with each plot receiving equal amounts of sun. Cover one plot with two inches of organic mulch, such as compost or ground bark. Leave the other plot uncovered. Use the same amount of water for each plot for two or three weeks. At the beginning of the experiment, and at one-week intervals, dig down and check the soil in each plot for moisture content. Which plot holds water better? Which plot shows better plant growth? (McCausland, 2006)
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.)
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