[dippogrk] Improving the Gregorian calendar

The Gregorian calendar omits a leap year (leap day) once every 400/3=133.3 years on the average.  However, based on the tropical year estimate of t=365.2421896698 days, the optimal frequency of omission is once every 1/(365.25-t)=128.036 years.  Therefore, we can radically improve the Gregorian calendar by omitting leap year once every 128 years.  The least disruptive way to do this would be to omit leap years on years which when divided by 128 leave a remainder of 52.  This makes 2100 a non-leap year (coinciding with the Gregorian calendar).  The first year which disagrees with the Gregorian calendar is 2200 (then 2228), giving us 188 years lead time to fix our calendars (and computers).

However, both the length of the year and length of the day are changing, not constant as the Gregorian calendar assumes.  A better non-disruptive improvement is, every 400 years, the decision of whether to have a leap year is determined by a formula, probably a polynomial or rational function (though maybe periodic components), whose coefficients are measured and updated over time.  One will probably have at least 200 years lead time when this "nonlinear-formula" calendar will deviate from the Gregorian calendar.  This scheme will fail if the tropical year becomes less than 365.24 days.