The ancient Greeks wondered when irrational numbers, like pi, can be represented with fractions. Two mathematicians now have a complete answer.

This is the business of rational approximation. Ancient mathematicians, for instance, recognized that the elusive ratio of a circle’s circumference to its diameter can be well approximated by the ...

First, decide on how close the approximation should be for fractions of a particular denominator. (Remember, the “numerator” refers to the top of a fraction and the “denominator” the bottom.

Scientists have calculated pi to 105 trillion digits, although most of us are more familiar with the approximation 3.14. But how do we know that pi is an irrational number?

Pi can be expressed as the fraction 22/7, which is an approximation of its actual value (hence the word "approximation" in the day's title). Source: Checkiday.com ...

S. ITO and H. NAKADA, On natural extensions of transformations related to Diophantine approximations, Proceedings of the Conference on Number Theory and Combinatorics, Japan 1984, World Scientific ...

Kurt Spielberg, Efficient Continued Fraction Approximations to Elementary Functions, Mathematics of Computation, Vol. 15, No. 76 (Oct., 1961), pp. 409-417 ...