Resources tagged with Continued fractions similar to Cocked Hat:
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Physics. Continued fractions. Surds. Mathematical reasoning & proof. Quadratic equations. Symmetry. Turning points. Graphs. Graph sketching. Golden ratio. Families of Graphs.There are 17 results
Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Continued fractions
Golden Mathematics
Age 16 to 18
A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
Good Approximations
Age 16 to 18 Challenge Level:
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Comparing Continued Fractions
Age 16 to 18 Challenge Level:
Which of these continued fractions is bigger and why?
Not Continued Fractions
Age 14 to 18 Challenge Level:
Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
Continued Fractions II
Age 16 to 18
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
Continued Fractions I
Age 14 to 18
An article introducing continued fractions with some simple puzzles for the reader.
Golden Fractions
Age 16 to 18 Challenge Level:
Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
Age 14 to 16
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
More Twisting and Turning
Age 11 to 16 Challenge Level:
It would be nice to have a strategy for disentangling any tangled ropes...
Infinite Continued Fractions
Age 16 to 18
In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.
Tangles
Age 11 to 16
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
There's a Limit
Age 14 to 18 Challenge 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?
Approximations, Euclid's Algorithm & Continued Fractions
Age 16 to 18
This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.
Resistance
Age 16 to 18 Challenge Level:
Find the equation from which to calculate the resistance of an infinite network of resistances.
Euclid's Algorithm and Musical Intervals
Age 16 to 18 Challenge Level:
Use Euclid's algorithm to get a rational approximation to the number of major thirds in an octave.
Symmetric Tangles
Age 14 to 16
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
NRICH is part of the family of activities in the Millennium Mathematics Project.