Editing Leap year (section)

==Gregorian calendar <span class="anchor" id="Algorithm"></span>==
{{See also|Gregorian calendar}}
[[File:Leap Centuries.jpg|thumb|upright|An image showing which century years are leap years in the Gregorian calendar]]
In the Gregorian calendar, the standard calendar in most of the world,<ref>{{Citation |last1=Dershowitz |first1=Nachum |title=Calendrical calculations |date=2008 |publisher=Cambridge University Press |first2=Edward M. |last2=Reingold |isbn=978-0-521-88540-9 |edition=3rd |location=Cambridge |page=45 |oclc=144768713 |quote="The calendar in use today in most of the world is the Gregorian or '[[Old Style and New Style dates|new-style]]' calendar designed by a commission assembled by Pope Gregory XIII in the sixteenth century."}}</ref> almost every fourth year is a leap year. Each leap year, the month of February has 29 days instead of 28. Adding one extra day in the calendar every four years compensates for the fact that a period of 365 days is shorter than a [[tropical year]] by almost six hours.<ref>{{citation |first1=Ed. K. Lee |last1=Lerner |first2=Brenda W. |last2=Lerner |title=Calendar |encyclopedia=The Gale Encyclopedia of Science |year=2004 |publisher=[[Gale]] |location=Detroit, MI }}</ref> However, this correction is excessive and the [[Gregorian calendar|Gregorian reform]] modified the Julian calendar's scheme of leap years as follows:
<blockquote>Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are.<ref>[http://aa.usno.navy.mil/faq/docs/calendars.php Introduction to Calendars] {{Webarchive|url=https://web.archive.org/web/20190613115330/http://aa.usno.navy.mil/faq/docs/calendars.php |date=2019-06-13 }}. (10 August 2017). [[United States Naval Observatory]].</ref></blockquote>

[[File:1800 calendar.jpg|thumb|upright|1800 calendar, showing that February had only 28&nbsp;days]]
Whereas the Julian calendar year incorrectly summarised Earth's tropical year as 365.25 days, the Gregorian calendar makes these exceptions to follow a calendar year of 365.2425 days. This more closely resembles a mean tropical year of 365.2422 days. Over a period of four centuries, the accumulated error of adding a leap day ''every'' four years amounts to about three extra days. The Gregorian calendar therefore omits three leap days every 400 years, which is the length of its ''leap cycle''. This is done by omitting 29 February in the three century years (multiples of 100) that are not multiples of 400.<ref name="usno">{{citation | author = United States Naval Observatory | author-link = United States Naval Observatory | date = 14 June 2011 | url = http://aa.usno.navy.mil/faq/docs/leap_years.php | title = Leap Years | access-date = 9 April 2014 | archive-date = 15 October 2007 | archive-url = https://web.archive.org/web/20071015174504/http://aa.usno.navy.mil/faq/docs/leap_years.php | url-status = dead }}</ref>{{sfn|Lerner|Lerner|2004|p=681}} The years 2000 and 2400 are leap years, but not 1700, 1800, 1900, 2100, 2200, and 2300. By this rule, an entire leap cycle is 400&nbsp;years, which totals 146,097 days, and the average number of days per year is 365&nbsp;+ {{Fraction|4}}&nbsp;− {{Fraction|100}}&nbsp;+ {{Fraction|400}}&nbsp;= 365&nbsp;+ {{Fraction|97|400}}&nbsp;= 365.2425.<ref name="auto">{{citation | last = Richards | first = E. G. | date = 2013 | chapter = Calendars | editor1-first = S. E. | editor1-last = Urban | editor2-first = P. K. | editor2-last = Seidelmann | title = Explanatory Supplement to the Astronomical Almanac | edition =3rd | location = Mill Valley, California | publisher = University Science Books | page = 598 | isbn = 9781891389856}}</ref> This rule could be applied to years before the Gregorian reform to create a [[proleptic Gregorian calendar]],<ref>{{citation | chapter-url = http://www.archive.org/stream/131123ExplanatorySupplementAstronomicalAlmanac/131123-explanatory-supplement-astronomical-almanac#page/n304/mode/1up | last = Doggett | first=L.E. | date=1992 | chapter = Calendars | editor-first = P. K. | editor-last = Seidelmann | title = Explanatory Supplement to the Astronomical Almanac | edition = 2nd | location = Sausalito, California | publisher = University Science Books | pages = 580–1}}</ref> though the result would not match any historical records.

{| width=640
|[[File:Gregoriancalendarleap solstice.svg]]<br />This graph shows the variations in date and time of the [[Solstice|June Solstice]].
|}
The Gregorian calendar was designed to keep the [[March equinox|vernal equinox]] on or close to 21 March, so that the date of [[Easter]] (celebrated on the Sunday after the ecclesiastical [[full moon]] that falls on or after 21 March) remains close to the vernal equinox.<ref>{{citation | first = E. G. | last = Richards | date = 1998 | title = Mapping time: The Calendar and its History | publisher = Oxford University Press | pages = 250–1 | isbn = 0-19-286205-7}}</ref> The "[[Gregorian calendar#Accuracy|Accuracy]]" section of the "[[Gregorian calendar]]" article discusses how well the Gregorian calendar achieves this objective, and how well it approximates the [[tropical year]].