ratFarey {numbers} | R Documentation |
Rational approximation of real numbers through Farey fractions.
ratFarey(x, n, upper = TRUE)
x |
real number. |
n |
integer, highest allowed denominator in a rational approximation. |
upper |
logical; shall the Farey fraction be grater than |
Rational approximation of real numbers through Farey fractions,
i.e. find for x
the nearest fraction in the Farey series of
rational numbers with denominator not larger than n
.
Returns a vector with two natural numbers, nominator and denominator.
Hardy, G. H., and E. M. Wright (1979). An Introduction to the Theory of Numbers. Fifth Edition, Oxford University Press, New York.
contFrac
ratFarey(pi, 100) # 22/7 0.0013 ratFarey(pi, 100, upper = FALSE) # 311/99 0.0002 ratFarey(-pi, 100) # -22/7 ratFarey(pi - 3, 70) # pi ~= 3 + (3/8)^2 ratFarey(pi, 1000) # 355/113 ratFarey(pi, 10000, upper = FALSE) # id. ratFarey(pi, 1e5, upper = FALSE) # 312689/99532 - pi ~= 3e-11 ratFarey(4/5, 5) # 4/5 ratFarey(4/5, 4) # 1/1 ratFarey(4/5, 4, upper = FALSE) # 3/4