Approximate a rational number that represents a decimal.
This function approximates a real number x using the Farey sequence method. It returns a Fraction object representing the closest approximation it can find within machine precision.
- The Farey sequence is used to find fractions close to a given real number.
- It iteratively finds the mediant of two fractions (the numerator and denominator of the mediant are the sums of the numerators and denominators of the two fractions, respectively) until it gets close enough to the target number.
- The mediant is a concept in mathematics, particularly in number theory, where it is defined as the fraction
(a+c)/(b+d)for two fractionsa/bandc/d.
- When this script is run as a main module, it calls
main()which in turn usesfareyto approximate a given real number and print the results.
For more information about the mediant and the Farey sequence, you might find these resources helpful: