A Matter of Appreciation
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Cut the Knot!, Alexander Bogomolny  
It is possible to learn to appreciate painting without being a painter... by analogy, it is possible to appreciate mathematics without being a mathematician. Appreciation does not require mastery, but it is impossible without adequate knowledge. Knowledge and mastery are labels at the two ends of a scale that stretches from the ability to recognize information through the ability to process it. Potential for appreciation is an increasing function on this scale. (Thus, if differentiable, the function has positive derivative. Furthermore, appreciation feeds on itself and, through a positive feedback loop, seeks to expand knowledge. It then follows that if the appreciation function is sufficiently smooth its second derivative is also positive.) The appreciation function depends on many parameters: disposition, perseverance, cultural surroundings, educational experience. The latter derives from the mathematical subjects themselves but even more from the manner in which mathematics has been presented... An elegant theorem was published by Giovanni Ceva in 1678... Ceva proved his theorem considering centers of gravity and the law of moments... 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:  Elementary, Middle School (68), High School (912) 
Languages:  English 
Resource Types:  Problems/Puzzles, Articles, Web Interactive/Java 
Math Topics:  Golden Ratio/Fibonacci, Triangles and Other Polygons 
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