Soap Films and Grid Walks
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Ivars Peterson (MathLand)  
A simple, physical demonstration of a mathematical truth can produce a lasting impression  one that inspires new questions and speculations. For Christopher C. Chang, a student at Henry M. Gunn Senior High School in Palo Alto, Calif., and one of 40 finalists in this year's Westinghouse Science Talent Search, that demonstration involved soap films and a classic problem invented nearly two centuries ago by Jakob Steiner, a professor at the University of Berlin. When Chang started to work on the Steiner problem, instead of finding Steiner points on a plane in which roads can go in any direction, he looked for them on a grid, meaning that the roads can go only in certain directions. This put the problem into the realm of discrete geometry.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles 
Math Topics:  Graph Theory, Convex/Discrete Geometry 
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