What Is Your Answer to That Question?
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Cut the Knot!, Alexander Bogomolny, with Don Greenwell  
The question  Why study mathematics?  appears in a multitude of guises and a plethora of variants... Mathematics is often compared to art. Like literature, mathematics has metaphor, ambiguity, paradox, and mystery. It has history. Mathematics has contributed mightily to philosophy. It has a sense of outcome, a feeling of rightness, a sense of catharsis. Like music, mathematics has harmony and dissonance. Also a discussion of Einstein's view on ugly and elegant proofs as related to the Menelaus theorem, and an example of how mathematics differs from its applications, involving an alternative derivation of Newton's method for finding square roots of positive numbers. With an exploration and proof of the candy problem (show that no matter how many pieces of candy each student has at the beginning, after a finite number of iterations all students have the same number of pieces of candy). An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem, one not stated directly since the applet is intended to be such that the right answer to an as yet unstated problem should be easy to surmise.  


Levels:  High School (912), College 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles, Web Interactive/Java 
Math Topics:  Graph Theory, Triangles and Other Polygons 
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