Thank you for the explanation. But I don't understand why there is a need to add a day every 100 years (except for years divisible by 400). Since the Gregorian calendar is only off by about 26 seconds per year, that adds up to less than an hour per century. One extra day ought to suffice for a long time -- over 3000 years as you point out.
The addition of a day is not in order to correct the 26-second variance of the Gregorian calendar with the actual length of the solar year. Rather, the opposite -- omitting three additional days every 400 years is in order to correct the Julian calendar. That is, three times every 400 years, we omit the day of February 29th from the calendar, and that is how the Gregorian calendar corrects the Julian calendar.
In other words, the way the Gregorian calendar is able to attan an accuracy of within 26 seconds to the actual length of the solar year, is by omitting the extra day three times out of every 400 years. It does not add an extra day to correct that 26 second discrepancy (rather, we just live with it, as you suggested!).
M. Kornfeld