Proofs in Mathematics
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Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny  
A discussion of the value of proofs in the classroom, followed by a collection of proofs classified as either simple or charming. Simple proofs: Number of vowels in a Lewis Carroll game; Pigeonhole Principle; Number of X's and O's; Coloring points in the plane; Averages of divisors; Breaking Chocolate Bars; Sqrt(2) is irrational; Halving a square; Longest segment; Shapes in a lattice; An integral. Charming proofs: A Checker  Jumping Problem; 4 Travellers Problem; Conic sections; Splitting piles; Three circles; Infinitude of Primes; Another three circles. Also Attractive facts: The Shoemaker's Knife; An Old Japanese Theorem; Carnot's Theorem; Ptolemy's Theorem; Orthocenters; Ford's touching circles; Napoleon's Theorem; A Property of a^n; Morley's Miracle; and References.  


Levels:  Middle School (68), High School (912), College 
Languages:  English 
Resource Types:  Lesson Plans and Activities, Problems/Puzzles 
Math Topics:  Euclidean Plane Geometry, Logic/Foundations, Number Theory 
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