Continued fractions and calendar systems
The necessary information from astronomy about a calendar is presented. Various known calendar systems is considered: the Julian calendar, the Jalali calendar, the Gregorian calendar, the Madler calendar, the revised Julian Calendar of Milankovitch. It is shown, according to Euler, that by expanding the length of the tropical year in a continued fraction, it is possible for its suitable fractions to get any known calendars, including the Revised Julian Calendar. The Revised Gregorian calendar is presented, more convenient and accurate than the Gregorian calendar, and the Jalali calendar. Super calendar is presented; it is the most accurate calendar up to date.