Proofs Without Words
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Cut the Knot!, Alexander Bogomolny  
Martin Gardner wrote, "There is no more effective aid in understanding certain algebraic identities than a good diagram. One should, of course, know how to manipulate algebraic symbols to obtain proofs, but in many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance." A historical discussion and illustrative applets, plus a simulation of an old puzzle (a farmer is to ferry across a river a goat, a cabbage, and a wolf). 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:  Games, Problems/Puzzles, Articles, Web Interactive/Java 
Math Topics:  Logic/Foundations 
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