Many industries rely on scale models to develop new products and designs. Architects, industrial designers, artists, clothing designers, and car manufacturers all use scale models. Each model is built to a scale that relates the actual object to the model through a ratio. Can you determine a formula for constructing a scale model? You can use your formula to make a model of your house, school, neighborhood, or town (CUBE, 2002). You can make scale models of the Wright Brothers aircraft…
Try different wind turbine/propeller (chord length, pitch) designs by making models from balsa wood. Connect the spinning axle to a DC motor and measure the voltage produced across a resistor to measure power output. Use fan as wind source. (Judge, 2004)
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…
The sustainability of our planet's resources ultimately depends upon our actions as citizens. How much we drive, what we eat, whether we have pets, and whether we recycle are all individual actions that affect the sustainability of the Earth's resources. Learn how ecological footprinting works and figure out how big your footprint is. How big is your family's footprint? Your school? A local business? Can you propose ways to increase or decrease the size of your ecological footprint? Develop…
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…
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…
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.
You probably know that you can use iron filings to reveal the magnetic field produced by a strong magnet. If you sandwich the iron filings between pieces of waxed paper, you can make a permanent record of your magnetic experiments (Gardner, 2004, 66). Cover the wax paper sandwich with a layer of brown paper (from a roll, or cut open a paper shopping bag), and then (with an adult's help) use a hot, dry iron to seal the waxed paper together. You will have to experiment a little with your iron…
A solution consists of a solute dissolved in a solvent. A solution is saturated when no additional solute will dissolve in it. Can a saturated solution of sodium chloride dissolve any Epsom salts? Can a saturated solution of Epsom salts dissolve any sodium chloride? How does solubility vary with temperature? How does solubility vary with the surface area of the solute? Design experiments to find out! (Gardner, 1999, 16-17, Stretton, 2004)
Some sequences of RNA can catalyze biochemical reactions, much like protein enzymes. These catalytic RNA sequences are called ribozymes. The function of a ribozyme depends upon the primary sequence of the RNA which folds into a 3-D structure. How do different ribozyme sequences fold? You can search for ribozyme sequences using Entrez BLAST (NCBI, 2006). Then you can use a program like MFOLD () to submit your sequence for an analysis of its predicted 3-D structures based upon thermodynamics…
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Very Long (1+ months)
Advanced biology course, or willingness to read up on such topics extensively.
A computer with Internet access is necessary for this project.
You can find this page online at: http://www.sciencebuddies.org/science-fair-projects/search.shtml?v=solt&pi=Math_p034
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