The application of continued fractions in Christiaan Huygens' planetarium

Comissioned by the minister of Finance of King Louis XIV, Christiaan Huygens designed a planetarium by using continued fractions to approximate the orbital periods of multiple planets. This planetarium was built by Johannes van Ceulen. An algorithm devised by Alexander Ostrowski can be used to prove that the approximation by convergents is, in a certain way, a best approximation possible. Another application of this algorithm is the gear train, in which convergents with large enumerators and denominators can be broken into two fractions. Eventually, this process leads to an improvement of the approximation used in Huygens' planetarium.Applied Mathematic