Leap Day a creation of tricky math and history
Leap Day, February 29, comes but once every four years. Leap Day is an adjustment to the calendar to cover up the difference between the time it takes the Earth to circle the sun and the usual 365-day year.
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The pope also tweaked the leap-year cycle to address the remaining one-day-per century drift: Years ending in "00" are not leap years unless they can be divided exactly by 400, so 2000 was a leap year, while 1900 was not. (Hence the 97 leap years over 400 years.)Skip to next paragraph
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Grabovsky has used continued fractions — fractions in which the denominator, or bottom number, is expressed as a whole number plus a fraction with its own denominator that is a whole number plus a fraction, and so on, iteratively — to examine the ways a calendar could be constructed to handle the discrepancy between the astronomical year and the calendar year.
The 400-year cycle Pope Gregory XIII installed accumulates an extra 26 seconds each year, resulting in an error of a full day every 3,320 years, he calculated. He compares this to a 500-year cycle, which would be 17 seconds shorter than the solar year, resulting in an error of one day each 5,031 years — an alternative the pope appears to have missed either because he didn't do his math or because astronomical measurements at the time weren't precise enough to justify this cycle, Grabovsky writes.
Another alternative, based on a 900-year cycle, is too complicated and has an inconveniently long cycle.
A tiny amount of error remains in the Gregorian calendar, and to correct for most of it, he recommends canceling leap year every 3,200 years.
"The new system would accumulate a one day error in 100,000 years, that is never," he writes as part of a presentation he gave on Feb. 29, 2000.
To add to the complication, the planet's speed along its orbit isn't constant, so occasionally, leap seconds are added to our clocks to compensate.
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