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Proofs in Mathematics

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Author:Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Description: 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 (6-8), High School (9-12), College
Languages: English
Resource Types: Lesson Plans and Activities, Problems/Puzzles
Math Topics: Euclidean Plane Geometry, Logic/Foundations, Number Theory

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