Leap Year 2016 and the Simple Yet Intricate Science of Leap Years

Summary: The simple yet intricate science of leap years accounts for leap year 2016 as one of the 21st century's 24 leap years.

German Jesuit mathematician and astronomer Christopher Clavius (March 25, 1538 to Feb. 3, 1612) gave critical input to Pope Gregory XIII, who introduced his namesake calendar in October 1582; the Gregorian Calendar stands as the most widely used civil calendar internationally: engraving by Jean Leclerc (1585 to 1633), after portrait by Francesco Villamena (1566 to 1624): Public Domain, via Wikimedia Commons

In the simple yet intricate science of leap years, Monday, Feb. 29, shows up in leap year 2016 as one of the 21st century’s 24 leap days because 2016 is divided cleanly, without remainders, by the number 4.

The intricacies of leap year science do not guarantee a leap year and its adjusting Feb. 29 leap day every four years. Within a century the trail of leaps predictably occurs every four years, but the century and millennium themselves operate according to an additional calculation.

Years marking human time's centuries and millennia end in double zeroes. It is not sufficient for double zero-ending years to respond with an exact division by 4. For example, the closing year of the 21st century, the year 2100, is not a leap year, even though 2100 divides cleanly by 4 to yield exactly 525.

As a year ending in double zeroes, however, 2100 has to pass the extra test of exact division by both 100 and 400 in order to achieve leap year status. Exact division of 2100 by 100 succeeds, by yielding a quotient, or result, of 21. But clean division by 400 fails, with a quotient of 5.25.

The clean division by both 100 and 400 creates a simple yet intricate pattern of one-on Feb. 29 leap day within a 400 year period for double zero-ending years. For example, years 1600, 2000 and 2400 all qualify as leap years.

The one-on leap year that ushers in a 400-year period signals three-off (no) leap days for the three succeeding double zero-ending years. For example, years 2100, 2200 and 2300 are excluded from leap year status.

An eight-year drought of no leap years characterizes the transition to and between the three leap-less double zero-ending years. For example, with 1900 as a leap-less year, the last leap year in the 19th century was 1896, and the next leap year did not occur until 1904.

Pope Gregory XIII, who served as Pope of the Catholic Church from May 13, 1572, to his death on April 10, 1585, and his astronomer-mathematician advisor, Christopher Clavius, devised the simple yet intricate system of leap years to resolve the mismatch that occurs naturally between the Earth’s orbit around the sun and human attempts to reflect that journey in a calendar, or annual timetable.

Earth requires approximately 365.25 days to complete its orbit of the Sun. The beginning of each orbit marks the start of a new year. A calendar displaying 365 days year after year is inaccurate by one-fourth of a day every year. The seemingly small inaccuracy grows by quarters every year until every four years the calendar is inaccurate by one day. In a century the inaccuracy bloats to 25 days. After six centuries, seasons drift by 150 days, or around five months, from their usual placement on the calendar. For example, seasonal drift exchanges the northern hemisphere's wintry January for a summery January.

The calendar devised by Pope Gregory XIII and his German Jesuit advisor is known as the Christian calendar, the Gregorian calendar or the Western calendar. It still stands internationally in the 21st century as the most widely used civil calendar.

The Gregorian calendar is a refinement of the superabundantly leap year-riddled Julian calendar. It is based on the tropical year. Daniel Brown, lecturer in astronomy at Nottingham Trent University in England’s East Midlands, explains:

“But as a very specific measure, one year, better described as a tropical year, is defined as the time between one spring equinox and the next being 365 days, five hours 48 minutes and 45 seconds.”

In the grandly simple yet intricate system of leap year science, the insertion of the Feb. 29 leap day serves as an adjustment, not as an addition of extra time. Brown credits ancient Greek astronomer and mathematician Hipparchus, considered as the founder of trigonometry, with recognizing over 2,000 years ago the inadequacy of expressing Earth’s natural orbit in a manmade time-telling system.

“This period is often rounded up to 365 and a quarter days -- although even the Greek astronomer Hipparchus realized over 2,000 years ago that this was a general approximation -- and so to keep our years aligned and reassuringly predictable, a leap day is added to the calendar every four years to allow for the accumulation of those otherwise overlooked four extra quarters,” explains Daniel Brown in his article, “Explainer: The Science Behind Leap Years and How They Work,” published Tuesday, Feb. 23, on The Conversation website.

February has 29 days in 2016: dwnews @dwnews, via Twitter Feb. 26, 2016

Acknowledgment

My special thanks to talented artists and photographers/concerned organizations who make their fine images available on the internet.

Image credits:

German Jesuit mathematician and astronomer Christopher Clavius (March 25, 1538 to Feb. 3, 1612) gave critical input to Pope Gregory XIII, who introduced his namesake calendar in October 1582; the Gregorian Calendar stands as the most widely used civil calendar internationally: engraving by Jean Leclerc (1585 to 1633), after portrait by Francesco Villamena (1566 to 1624): Public Domain, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Christopher_Clavius.jpg;
No copyright -- United States, via Smithsonian Institution Libraries (SIL) @ https://library.si.edu/image-gallery/73149

February has 29 days in 2016: dwnews @dwnews, via Twitter Feb. 26, 2016, @ https://twitter.com/dwnews/status/703249944174469120

For further information:

Abbany, Zulfikar. "No perfect calendar: why we have leap years and why the Earth's always out of sync." DW (Deutsche Welle) > Top Stories > Sci-Tech. Feb. 26, 2016.
Available @ http://www.dw.com/en/no-perfect-calendar-why-we-have-leap-years-and-why-the-earths-always-out-of-sync/a-19077064

Brown, Daniel. "Explainer: the science behind leap years and how they work." The Conversation > Science & Technology. Feb. 23, 2016.
Available @ https://theconversation.com/explainer-the-science-behind-leap-years-and-how-they-work-54788

dwnews @dwnews. "February 29? Why we have a #leapyear and why the Earth is always out of sync." Twitter. Feb. 26, 2016.
Available @ https://twitter.com/dwnews/status/703249944174469120

Vox. "How leap year works." YouTube. Feb. 27, 2016.
Available @ https://www.youtube.com/watch?v=YTOr8_ILqGw