Continued fractions
problem
More Twisting and Turning
It would be nice to have a strategy for disentangling any tangled ropes...
problem
Resistance
Find the equation from which to calculate the resistance of an
infinite network of resistances.
problem
Euclid's Algorithm and Musical Intervals
Use Euclid's algorithm to get a rational approximation to the
number of major thirds in an octave.
problem
Golden Fractions
Find the link between a sequence of continued fractions and the
ratio of succesive Fibonacci numbers.
problem
Not Continued Fractions
Which rational numbers cannot be written in the form x + 1/(y +
1/z) where x, y and z are integers?
problem
There's a limit
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?
problem
Good Approximations
Solve quadratic equations and use continued fractions to find
rational approximations to irrational numbers.
article
Symmetric Tangles
The tangles created by the twists and turns of the Conway rope
trick are surprisingly symmetrical. Here's why!