article
Infinite Continued Fractions
In this article we are going to look at infinite continued
fractions - continued fractions that do not terminate.
Continued fractions
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problemGood Approximations
Age16 to 18Challenge level
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers. -
problemFavouriteThere's a Limit
Age14 to 18Challenge level
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely? -
problemComparing Continued Fractions
Age16 to 18Challenge level
Which of these continued fractions is bigger and why? -
problemEuclid's Algorithm and Musical Intervals
Age16 to 18Challenge level
Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave. -
problemGolden Fractions
Age16 to 18Challenge level
Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers. -
problemResistance
Age16 to 18Challenge level
Find the equation from which to calculate the resistance of an infinite network of resistances.