An Introduction to Continued Fractions
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|Continued fractions are just another way of writing fractions. They have some interesting links with a jigsaw-puzzle problem of splitting a rectangle up into squares and also with one of the oldest algorithms known to mathematicians - Euclid's Algorithm for computing greatest common divisors (GCD)." Contents: A jigsaw puzzle: splitting rectangles into squares; The General form of a Continued Fraction - List Notation for Continued Fractions; Continued Fractions and Euclid's GCD Algorithm - Euclid's GCD algorithm, Using Lists of Divisors to find the GCD; Continued Fractions for decimal fractions - Terminating Decimal fractions, Continued fractions for square roots; Solving Quadratics with Continued Fractions - The Golden section and a quadratic equation; The Silver Means - Numerical values of the Silver Means, Exact values of the Silver Means; Other numbers with patterns in their CF; A link between The Golden string, Continued Fractions and The Fibonacci Series; Links and References.|
|Levels:||High School (9-12), College|
|Resource Types:||Lesson Plans and Activities, Problems/Puzzles|
|Math Topics:||Equations, Golden Ratio/Fibonacci, Number Theory, Fibonacci Sequence|
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