In the United States, lighting for homes accounts for about 14% of all residential electricity usage (EIA, 2014). That's billions of dollars worth of electricity per year. The U.S. has passed legislation to phase out older, more inefficient incandescent light bulbs, and they are being replaced with newer, more-efficient bulb types like compact fluorescent lights (CFLs) or light-emitting diodes (LEDs). How much energy (measured in kilowatt-hours [kWh]) and how much money could be saved by…
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How much water do you use? Conserving water can do more than save your parents' money, it can also save freshwater ecosystems, wetlands, and watersheds. Some companies are trying to help fix the problem by making low flow faucets and showerheads. How well do they work? How much water can you save? Go to the hardware store to buy a few of the water saving products. Compare the amount of water that you run over a period of time to determine how much water you can save. Which water saving…
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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…
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Can computer games be used to educate? Pick a game that incorporates educational material. There are a variety of educational computer games on the market in the areas of math, history, science, and language, as well as many simpler versions free on the Internet. Make up a test based on the subject area covered by the computer game. Have your volunteers take the test before and after playing the game. Does playing the computer game improve people's score on the test?
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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 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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Compare the strengths and weaknesses of different digital image formats. How does the amount of compression affect a JPEG image? What happens when you save a JPEG image multiple times?
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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…
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Is soil structure an important factor in earthquake dynamics? Investigate soil liquefaction and how different soil types respond to earthquake movements. Are movements more dramatic in sandy/loamy or clay type soils? Which soil structures are most stable? Which are the most volatile? (MCEER, 2005)
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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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