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Improved Calendar

Further to Russell Dear's calendar puzzle [Neurobics, Oct]:

The Gregorian calendar dictates that year 2000 AD shall be a leap year, i.e. a year that contains 366 days, with an additional day to offset the difference between the common year (365 days) and the astronomical year (365 1/4 days). This occurs every fourth year, with the exception of centenary years not divisible by 400.

Under this system the average year is 365 + 1/4 - 1/100 + 1/400 = 365.2425 days.

However, the calendar (tropical, solar) year is more accurately 365.24220 days.

It would appear that the calendar would have been slightly improved (or more accurate) if centenary years not divisible by 500 (contrasted to 400) were decreed leap years. Average year is then 365 + 1/4 - 1/100 + 1/500 = 365.2420 days.

Rather better than either of these systems would be 8 leap years per every 33 years only, 365.2424 days.

Possibly the ultimate calendar, obtained by continued fraction convergents, has 31 leap years per 128 years, 365.24219 days.

Don S. McDonald, Wellington