I couldn’t resist posting on February 29th a little piece I wrote, well, about four years ago…

February 29^{th} has come and gone with its usual fanfare being celebrated quadrennially. That is, except every century when we skip the leap day, except every four centuries when we keep it.

Huh? Perhaps I should back up a bit…

Our typical calendar year is 365 days (or 8760 hours, 525,600 minutes, 31,536,000 seconds, you get the point…) but our actual solar year, i.e. the time it takes the Earth to make one rotation around the sun, is approximately 365.242190419 days. If we were to keep using 365 days per year, after a century December 31^{st} would act a lot like a typical December 7^{th} because we would be 24 days behind. After 1000 years, we would be off by 242 days and celebrating New Year’s Day at a time when spring was just getting into full swing. This is clearly a problem! Hence, the “Leap Day” of February 29^{th}. Adding this every four years and our average calendar year becomes 365.25 days. A much better result, but clearly we can do better! To trim that average to 364.24 days, we skip the Leap Day every one hundred years. So why, you may ask, did we have a leap day in 2000? We celebrated this quadricentennial event because an average of 365.24 days is just not good enough! By adding that leap day back every 400 years, our average calendar year becomes 365.2425 days. This amounts to a deviation of 26.7 seconds per year or 0.0000848% and a *much* better result. Of course, after 3200 years of this, we would be off by an entire day again, but that debate can wait a couple millennia.